Inventiones mathematicae, ISSN 0020-9910, 7/2014, Volume 197, Issue 1, pp. 115 - 213

We establish nonlinear stability and asymptotic behavior of traveling periodic waves of viscous conservation laws under localized perturbations or nonlocalized perturbations asymptotic to constant...

35B10 | Mathematics, general | Mathematics | 35B40 | 35B35 | 35L65 | ROLL-WAVES | MATHEMATICS | TRAVELING-WAVE SOLUTIONS | HYPERBOLIC-PARABOLIC-SYSTEMS | FILM FLOW | NONLINEAR STABILITY | SPECTRAL STABILITY | REACTION-DIFFUSION WAVES | DYNAMICS | SHOCK-WAVES | ASYMPTOTIC-BEHAVIOR | Environmental law | Conservation laws | Stability | Perturbation methods | Asymptotic properties | Mathematical analysis | Modulation | Nonlinearity | Constants | Analysis of PDEs

35B10 | Mathematics, general | Mathematics | 35B40 | 35B35 | 35L65 | ROLL-WAVES | MATHEMATICS | TRAVELING-WAVE SOLUTIONS | HYPERBOLIC-PARABOLIC-SYSTEMS | FILM FLOW | NONLINEAR STABILITY | SPECTRAL STABILITY | REACTION-DIFFUSION WAVES | DYNAMICS | SHOCK-WAVES | ASYMPTOTIC-BEHAVIOR | Environmental law | Conservation laws | Stability | Perturbation methods | Asymptotic properties | Mathematical analysis | Modulation | Nonlinearity | Constants | Analysis of PDEs

Journal Article

Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 12/2014, Volume 65, Issue 6, pp. 1167 - 1188

... ) limit of a 3D conservation laws derived from the well-known Keller–Segel model. First, we establish the global well-posedness of classical solutions to the Cauchy...

Conservation laws | Engineering | Mathematical Methods in Physics | Large amplitude solution | 35Q99 | Convergence rate | 92C17 | Theoretical and Applied Mechanics | 35M99 | Zero diffusion limit | Chemotaxis | 35L65 | EXISTENCE | MATHEMATICS, APPLIED | BOUNDARY-LAYERS | HALF-PLANE | MODELING CHEMOTAXIS | TRAVELING-WAVES | VISCOSITY LIMIT | NAVIER-STOKES EQUATIONS | NONLINEAR STABILITY | HYPERBOLIC-PARABOLIC SYSTEM | REINFORCED RANDOM-WALKS | Environmental law | Norms | Oscillations | Mathematical models | Diffusion | Three dimensional | Convergence | Cauchy problem | Mathematics - Analysis of PDEs

Conservation laws | Engineering | Mathematical Methods in Physics | Large amplitude solution | 35Q99 | Convergence rate | 92C17 | Theoretical and Applied Mechanics | 35M99 | Zero diffusion limit | Chemotaxis | 35L65 | EXISTENCE | MATHEMATICS, APPLIED | BOUNDARY-LAYERS | HALF-PLANE | MODELING CHEMOTAXIS | TRAVELING-WAVES | VISCOSITY LIMIT | NAVIER-STOKES EQUATIONS | NONLINEAR STABILITY | HYPERBOLIC-PARABOLIC SYSTEM | REINFORCED RANDOM-WALKS | Environmental law | Norms | Oscillations | Mathematical models | Diffusion | Three dimensional | Convergence | Cauchy problem | Mathematics - Analysis of PDEs

Journal Article

Memoirs of the American Mathematical Society, ISSN 0065-9266, 03/2015, Volume 234, Issue 1105, pp. 1 - 178

We study the perturbation of a shock wave in conservation laws with physical viscosity...

Conservation laws | Nonlinear stability | Shock waves | Physical viscosity | Magneto-hydrodynamics | Green's function | Pointwise estimates | Wave interactions | Compressible navier-stokes equations | Large time behavior | Quasilinear hyperbolic-parabolic systems | FADING MEMORY | wave interactions | compressible Navier-Stokes equations | magneto-hydrodynamics | STABILITY | LARGE-TIME BEHAVIOR | pointwise estimates | MATHEMATICS | nonlinear stability | NAVIER-STOKES EQUATIONS | HYPERBOLIC-PARABOLIC-SYSTEMS | physical viscosity | large time behavior | quasilinear hyperbolic-parabolic systems | shock waves

Conservation laws | Nonlinear stability | Shock waves | Physical viscosity | Magneto-hydrodynamics | Green's function | Pointwise estimates | Wave interactions | Compressible navier-stokes equations | Large time behavior | Quasilinear hyperbolic-parabolic systems | FADING MEMORY | wave interactions | compressible Navier-Stokes equations | magneto-hydrodynamics | STABILITY | LARGE-TIME BEHAVIOR | pointwise estimates | MATHEMATICS | nonlinear stability | NAVIER-STOKES EQUATIONS | HYPERBOLIC-PARABOLIC-SYSTEMS | physical viscosity | large time behavior | quasilinear hyperbolic-parabolic systems | shock waves

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 08/2017, Volume 159, pp. 208 - 263

Global existence for multicomponent reactive fluids with fast chemistry is investigated. The system of partial differential equations derived from the kinetic...

Multicomponent | Fast-chemistry | Hyperbolic–parabolic | EXISTENCE | MATHEMATICS, APPLIED | EQUATIONS | THERMAL NONEQUILIBRIUM | EQUILIBRIUM STATES | STEADY-STATE APPROXIMATION | MATHEMATICS | PARABOLIC-SYSTEMS | HYPERBOLIC CONSERVATION-LAWS | Hyperbolic-parabolic | MULTICOMPONENT REACTIVE FLOWS | ENTROPY

Multicomponent | Fast-chemistry | Hyperbolic–parabolic | EXISTENCE | MATHEMATICS, APPLIED | EQUATIONS | THERMAL NONEQUILIBRIUM | EQUILIBRIUM STATES | STEADY-STATE APPROXIMATION | MATHEMATICS | PARABOLIC-SYSTEMS | HYPERBOLIC CONSERVATION-LAWS | Hyperbolic-parabolic | MULTICOMPONENT REACTIVE FLOWS | ENTROPY

Journal Article

Communications on Pure and Applied Mathematics, ISSN 0010-3640, 11/1998, Volume 51, Issue 11-12, pp. 1397 - 1424

We consider systems of conservation laws and give conditions for nonlinear stability of viscous shock profiles...

MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCE | WAVES | STEADY-STATE | HYPERBOLIC-PARABOLIC-SYSTEMS

MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCE | WAVES | STEADY-STATE | HYPERBOLIC-PARABOLIC-SYSTEMS

Journal Article

Boundary Value Problems, ISSN 1687-2762, 12/2016, Volume 2016, Issue 1, pp. 1 - 9

This paper is concerned with the existence of traveling waves for the scalar hyperbolic-parabolic balance law...

Ordinary Differential Equations | Analysis | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | discontinuous traveling waves | Mathematics | scalar hyperbolic-parabolic balance law | entropy solution | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | STABILITY | BEHAVIOR | TIME | VISCOUS CONSERVATION-LAWS | Boundary value problems | Usage | Research | Traveling-wave tubes | Perturbation (Mathematics) | Tests, problems and exercises | Construction | Balancing | Mathematical analysis | Texts | Scalars | Traveling waves | Entropy

Ordinary Differential Equations | Analysis | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | discontinuous traveling waves | Mathematics | scalar hyperbolic-parabolic balance law | entropy solution | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | STABILITY | BEHAVIOR | TIME | VISCOUS CONSERVATION-LAWS | Boundary value problems | Usage | Research | Traveling-wave tubes | Perturbation (Mathematics) | Tests, problems and exercises | Construction | Balancing | Mathematical analysis | Texts | Scalars | Traveling waves | Entropy

Journal Article

Communications in Mathematical Sciences, ISSN 1539-6746, 2017, Volume 15, Issue 4, pp. 1073 - 1106

This paper studies the stability of smooth traveling wave solutions to a nonlinear PDE problem in reducing image noise. Specifically, we prove that the...

Nonlinear stability | Rate of decay | Nonlinear conservation laws | Image processing | Weighted energy estimates | image processing | SHOCK PROFILES | MATHEMATICS, APPLIED | CHEMOTAXIS | EQUATIONS | nonlinear conservation laws | rate of decay | nonlinear stability | DYNAMICS | DIFFUSION | ASYMPTOTIC STABILITY | HYPERBOLIC-PARABOLIC SYSTEM | NOISE REMOVAL | weighted energy estimates | NONCONVEX RELAXATION | CONVERGENCE-RATES

Nonlinear stability | Rate of decay | Nonlinear conservation laws | Image processing | Weighted energy estimates | image processing | SHOCK PROFILES | MATHEMATICS, APPLIED | CHEMOTAXIS | EQUATIONS | nonlinear conservation laws | rate of decay | nonlinear stability | DYNAMICS | DIFFUSION | ASYMPTOTIC STABILITY | HYPERBOLIC-PARABOLIC SYSTEM | NOISE REMOVAL | weighted energy estimates | NONCONVEX RELAXATION | CONVERGENCE-RATES

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 05/2016, Volume 67, Issue 2, pp. 618 - 643

This work is concerned by the numerical approximation of the weak solutions of a system of partial differential equations arising when modeling the movements...

Well-balanced schemes | Mixed hyperbolic/parabolic PDE | Finite volume method of Godunov type | Chemotaxis model | Asymptotic preserving schemes | MATHEMATICS, APPLIED | GENERALIZED RIEMANN PROBLEM | KINETIC-EQUATIONS | ASYMPTOTIC PRESERVING SCHEME | DIFFUSIVE REGIMES | SHALLOW-WATER EQUATIONS | GODUNOV-TYPE SCHEMES | RADIATIVE-TRANSFER | SOURCE TERMS | NUMERICAL SCHEME | CONSERVATION-LAWS | Analysis | Models | Differential equations | Approximation | Movements | Partial differential equations | Asymptotic properties | Mathematical analysis | Preserves | Mathematical models | Hyperbolic systems

Well-balanced schemes | Mixed hyperbolic/parabolic PDE | Finite volume method of Godunov type | Chemotaxis model | Asymptotic preserving schemes | MATHEMATICS, APPLIED | GENERALIZED RIEMANN PROBLEM | KINETIC-EQUATIONS | ASYMPTOTIC PRESERVING SCHEME | DIFFUSIVE REGIMES | SHALLOW-WATER EQUATIONS | GODUNOV-TYPE SCHEMES | RADIATIVE-TRANSFER | SOURCE TERMS | NUMERICAL SCHEME | CONSERVATION-LAWS | Analysis | Models | Differential equations | Approximation | Movements | Partial differential equations | Asymptotic properties | Mathematical analysis | Preserves | Mathematical models | Hyperbolic systems

Journal Article

Bulletin of the Brazilian Mathematical Society, New Series, ISSN 1678-7544, 6/2016, Volume 47, Issue 2, pp. 619 - 630

In the present paper, we show the existence and asymptotic stability of a stationary solution for a system of viscous conservation laws in a one-dimensional half space...

stationary waves | 76N15 | 35B35 | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | 35B40 | compressible viscous gases | SPACE | MATHEMATICS | HYPERBOLIC-PARABOLIC-SYSTEMS | STABILITY | EQUATIONS | CONVERGENCE RATE | Environmental law

stationary waves | 76N15 | 35B35 | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | 35B40 | compressible viscous gases | SPACE | MATHEMATICS | HYPERBOLIC-PARABOLIC-SYSTEMS | STABILITY | EQUATIONS | CONVERGENCE RATE | Environmental law

Journal Article

AIMS MATHEMATICS, ISSN 2473-6988, 2018, Volume 3, Issue 1, pp. 35 - 43

In this paper, we study a system of viscous conservation laws given by a form of a symmetric parabolic system...

boundary layer solutions | energy method | center manifold theory | EXISTENCE | MATHEMATICS, APPLIED | stationary waves | compressible viscous gases | HYPERBOLIC-PARABOLIC SYSTEMS | SPACE | MATHEMATICS | WAVES | NAVIER-STOKES EQUATIONS | CONVERGENCE RATE

boundary layer solutions | energy method | center manifold theory | EXISTENCE | MATHEMATICS, APPLIED | stationary waves | compressible viscous gases | HYPERBOLIC-PARABOLIC SYSTEMS | SPACE | MATHEMATICS | WAVES | NAVIER-STOKES EQUATIONS | CONVERGENCE RATE

Journal Article

Journal of Hyperbolic Differential Equations, ISSN 0219-8916, 03/2010, Volume 7, Issue 1, pp. 1 - 67

We consider a class of doubly nonlinear degenerate hyperbolic-parabolic equations with homogeneous Dirichlet boundary conditions, for which we first establish...

Finite volume scheme | Conservation law | Discrete duality | LerayLions type operator | Uniqueness | Non-Lipschitz flux | Degenerate hyperbolic-parabolic equation | Existence | Convergence | Entropy solution | RENORMALIZED SOLUTIONS | MATHEMATICS, APPLIED | discrete duality | APPROXIMATION | convergence | DIFFUSION OPERATORS | existence | WELL-POSEDNESS | PHYSICS, MATHEMATICAL | BV SOLUTIONS | finite volume scheme | ENTROPY SOLUTIONS | Leray-Lions type operator | uniqueness | conservation law | SCALAR CONSERVATION-LAWS | entropy solution | non-Lipschitz flux | CONTINUOUS DEPENDENCE | Construction | Approximation | Boundary conditions | Entropy | Entropy of solution | Estimates | Mathematical analysis | Dissipation | Inequalities | Proving | Dirichlet problem | Nonlinearity

Finite volume scheme | Conservation law | Discrete duality | LerayLions type operator | Uniqueness | Non-Lipschitz flux | Degenerate hyperbolic-parabolic equation | Existence | Convergence | Entropy solution | RENORMALIZED SOLUTIONS | MATHEMATICS, APPLIED | discrete duality | APPROXIMATION | convergence | DIFFUSION OPERATORS | existence | WELL-POSEDNESS | PHYSICS, MATHEMATICAL | BV SOLUTIONS | finite volume scheme | ENTROPY SOLUTIONS | Leray-Lions type operator | uniqueness | conservation law | SCALAR CONSERVATION-LAWS | entropy solution | non-Lipschitz flux | CONTINUOUS DEPENDENCE | Construction | Approximation | Boundary conditions | Entropy | Entropy of solution | Estimates | Mathematical analysis | Dissipation | Inequalities | Proving | Dirichlet problem | Nonlinearity

Journal Article

Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 11/2013, Volume 23, Issue 12, pp. 2193 - 2251

We investigate a system of partial differential equations modeling supercritical multicomponent reactive fluids. These equations involve nonideal fluid...

nonideal | supercritical | Multicomponent reactive flow | stability | MATHEMATICS, APPLIED | MODIFIED ENSKOG EQUATION | LARGE-TIME BEHAVIOR | EQUATION-OF-STATE | HYPERBOLIC-PARABOLIC-SYSTEMS | NAVIER-STOKES EQUATIONS | TRANSPORT ALGORITHMS | CONSERVATION-LAWS | ASYMPTOTIC STABILITY | IRREVERSIBLE-PROCESSES | NUMERICAL-SIMULATION

nonideal | supercritical | Multicomponent reactive flow | stability | MATHEMATICS, APPLIED | MODIFIED ENSKOG EQUATION | LARGE-TIME BEHAVIOR | EQUATION-OF-STATE | HYPERBOLIC-PARABOLIC-SYSTEMS | NAVIER-STOKES EQUATIONS | TRANSPORT ALGORITHMS | CONSERVATION-LAWS | ASYMPTOTIC STABILITY | IRREVERSIBLE-PROCESSES | NUMERICAL-SIMULATION

Journal Article

13.
Full Text
Asymptotic dynamics on a singular chemotaxis system modeling onset of tumor angiogenesis

Journal of Differential Equations, ISSN 0022-0396, 2016, Volume 260, Issue 3, pp. 2225 - 2258

The asymptotic behavior of solutions to a singular chemotaxis system modeling the onset of tumor angiogenesis in two and three dimensional whole spaces is...

Tumor angiogenesis | Decay estimates | Energy estimates | Global well-posedness | Chemotaxis | GLOBAL EXISTENCE | DECAY | WELL-POSEDNESS | MHD EQUATIONS | TRAVELING-WAVES | MATHEMATICS | KELLER-SEGEL SYSTEM | NONLINEAR STABILITY | CONSERVATION-LAWS | HYPERBOLIC-PARABOLIC SYSTEM | Analysis | Models | Tumors

Tumor angiogenesis | Decay estimates | Energy estimates | Global well-posedness | Chemotaxis | GLOBAL EXISTENCE | DECAY | WELL-POSEDNESS | MHD EQUATIONS | TRAVELING-WAVES | MATHEMATICS | KELLER-SEGEL SYSTEM | NONLINEAR STABILITY | CONSERVATION-LAWS | HYPERBOLIC-PARABOLIC SYSTEM | Analysis | Models | Tumors

Journal Article

14.
Full Text
Continuous dependence estimates for nonlinear fractional convection-diffusion equations

SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2012, Volume 44, Issue 2, pp. 603 - 632

.... Estimates of the rates of convergence for general nonlinear nonlocal vanishing viscosity approximations of scalar conservation laws then follow as a corollary...

Pure jump Lévy processes | Entropy solutions | Fractional conservation laws | Fractal conservation laws | Continuous dependence estimates | Mixed hyperbolic parabolic equations | Nonlinear parabolic equations | MATHEMATICS, APPLIED | continuous dependence estimates | mixed hyperbolic parabolic equations | entropy solutions | MODEL | GLOBAL WELL-POSEDNESS | FRACTAL BURGERS EQUATIONS | DEGENERATE PARABOLIC EQUATIONS | pure jump Levy processes | POROUS-MEDIUM EQUATION | fractal conservation laws | CHAPMAN-ENSKOG EXPANSION | nonlinear parabolic equations | fractional conservation laws | ASYMPTOTICS | CONSERVATION-LAWS | REGULARIZATION | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

Pure jump Lévy processes | Entropy solutions | Fractional conservation laws | Fractal conservation laws | Continuous dependence estimates | Mixed hyperbolic parabolic equations | Nonlinear parabolic equations | MATHEMATICS, APPLIED | continuous dependence estimates | mixed hyperbolic parabolic equations | entropy solutions | MODEL | GLOBAL WELL-POSEDNESS | FRACTAL BURGERS EQUATIONS | DEGENERATE PARABOLIC EQUATIONS | pure jump Levy processes | POROUS-MEDIUM EQUATION | fractal conservation laws | CHAPMAN-ENSKOG EXPANSION | nonlinear parabolic equations | fractional conservation laws | ASYMPTOTICS | CONSERVATION-LAWS | REGULARIZATION | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2020, Volume 268, Issue 4, pp. 1379 - 1411

.... We study Cauchy problem for the original system and its transformed system, which is one of hyperbolic-parabolic balance laws...

Logarithmic sensitivity | Chemotaxis | Logistic growth | Optimal time decay rates | Cauchy problem | EXISTENCE | MATHEMATICAL-ANALYSIS | BOUNDEDNESS | GLOBAL ASYMPTOTIC STABILITY | TRAVELING-WAVES | MATHEMATICS | SINGULAR SENSITIVITY | NONLINEAR STABILITY | CONSTANT EQUILIBRIA | CONSERVATION-LAWS | HYPERBOLIC-PARABOLIC SYSTEM

Logarithmic sensitivity | Chemotaxis | Logistic growth | Optimal time decay rates | Cauchy problem | EXISTENCE | MATHEMATICAL-ANALYSIS | BOUNDEDNESS | GLOBAL ASYMPTOTIC STABILITY | TRAVELING-WAVES | MATHEMATICS | SINGULAR SENSITIVITY | NONLINEAR STABILITY | CONSTANT EQUILIBRIA | CONSERVATION-LAWS | HYPERBOLIC-PARABOLIC SYSTEM

Journal Article

Mathematical Biosciences, ISSN 0025-5564, 12/2012, Volume 240, Issue 2, pp. 161 - 168

.... ► We transform the model, via a smart Hopf-Cole transformation, into a system of conservation laws without singularity...

Conservation laws | Nonlinear stability | Traveling waves | Chemotaxis | Asymptotic behavior | Wave speed | BACTERIA | INSTABILITY | ANGIOGENESIS | EQUATIONS | TRAVELING-WAVES | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | VISCOUS SHOCK-WAVES | DIFFUSION | CONSERVATION-LAWS | HYPERBOLIC-PARABOLIC SYSTEM | Neovascularization, Physiologic - physiology | Chemotaxis - physiology | Models, Biological | Computer Simulation | Models | Wave propagation | Environmental law | Analysis

Conservation laws | Nonlinear stability | Traveling waves | Chemotaxis | Asymptotic behavior | Wave speed | BACTERIA | INSTABILITY | ANGIOGENESIS | EQUATIONS | TRAVELING-WAVES | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | VISCOUS SHOCK-WAVES | DIFFUSION | CONSERVATION-LAWS | HYPERBOLIC-PARABOLIC SYSTEM | Neovascularization, Physiologic - physiology | Chemotaxis - physiology | Models, Biological | Computer Simulation | Models | Wave propagation | Environmental law | Analysis

Journal Article

Kinetic and Related Models, ISSN 1937-5093, 2012, Volume 5, Issue 3, pp. 563 - 581

In this paper, we investigate large amplitude solutions to a system of conservation laws which is transformed, by a change of variable, from the well-known Keller-Segel model describing cell (bacteria...

Conservation laws | Convergence rate | Zero diffusion limit | Chemotaxis | Large amplitude solution | MATHEMATICS, APPLIED | BACTERIA | GLOBAL EXISTENCE | large amplitude solution | BOUNDARY-LAYERS | HALF-PLANE | TRAVELING-WAVES | VISCOSITY LIMIT | MATHEMATICS | NAVIER-STOKES EQUATIONS | NONLINEAR STABILITY | zero diffusion limit | convergence rate | HYPERBOLIC-PARABOLIC SYSTEM | REINFORCED RANDOM-WALKS | chemotaxis

Conservation laws | Convergence rate | Zero diffusion limit | Chemotaxis | Large amplitude solution | MATHEMATICS, APPLIED | BACTERIA | GLOBAL EXISTENCE | large amplitude solution | BOUNDARY-LAYERS | HALF-PLANE | TRAVELING-WAVES | VISCOSITY LIMIT | MATHEMATICS | NAVIER-STOKES EQUATIONS | NONLINEAR STABILITY | zero diffusion limit | convergence rate | HYPERBOLIC-PARABOLIC SYSTEM | REINFORCED RANDOM-WALKS | chemotaxis

Journal Article

MATHEMATICAL BIOSCIENCES AND ENGINEERING, ISSN 1547-1063, 2020, Volume 17, Issue 2, pp. 1413 - 1427

We present an analytic framework where biological pest control can be simulated. Control is enforced through the choice of a time and space dependent function...

predator-prey dynamics | NUMERICAL-SOLUTION | control of conservation laws | MATHEMATICAL & COMPUTATIONAL BIOLOGY | non-local balance laws | biological pest control | mixed hyperbolic-parabolic systems

predator-prey dynamics | NUMERICAL-SOLUTION | control of conservation laws | MATHEMATICAL & COMPUTATIONAL BIOLOGY | non-local balance laws | biological pest control | mixed hyperbolic-parabolic systems

Journal Article

Chemical Engineering Journal, ISSN 1385-8947, 2000, Volume 80, Issue 1, pp. 91 - 104

For one space dimension, the phenomenological theory of sedimentation of flocculated suspensions yields a model that consists of an initial-boundary value...

Mixed hyperbolic–parabolic PDE | Settling of flocculated suspensions | Operator splitting | Numerical simulation | Initial-boundary value problem | Sedimentation | Finite difference method | DISCONTINUOUS FLUX FUNCTION | CONTINUOUS SEDIMENTATION | BEHAVIOR | initial-boundary value problem | finite difference method | sedimentation | ENGINEERING, CHEMICAL | CONSOLIDATION | ENGINEERING, ENVIRONMENTAL | SCALAR CONSERVATION-LAWS | BOUNDARY-VALUE-PROBLEM | POINT-SOURCE | PARTICULATE SYSTEMS | settling of flocculated suspensions | operator splitting | GLOBAL WEAK SOLUTIONS | numerical simulation | mixed hyperbolic-parabolic PDE | VELOCITIES

Mixed hyperbolic–parabolic PDE | Settling of flocculated suspensions | Operator splitting | Numerical simulation | Initial-boundary value problem | Sedimentation | Finite difference method | DISCONTINUOUS FLUX FUNCTION | CONTINUOUS SEDIMENTATION | BEHAVIOR | initial-boundary value problem | finite difference method | sedimentation | ENGINEERING, CHEMICAL | CONSOLIDATION | ENGINEERING, ENVIRONMENTAL | SCALAR CONSERVATION-LAWS | BOUNDARY-VALUE-PROBLEM | POINT-SOURCE | PARTICULATE SYSTEMS | settling of flocculated suspensions | operator splitting | GLOBAL WEAK SOLUTIONS | numerical simulation | mixed hyperbolic-parabolic PDE | VELOCITIES

Journal Article

Journal de mathématiques pures et appliquées, ISSN 0021-7824, 10/2019, Volume 130, pp. 251 - 287

Though the boundary layer formation in the chemotactic process has been observed in experiment (cf. [63]), the mathematical study on the boundary layer...

Logarithmic singularity | Energy estimates | Chemotaxis | Boundary layers | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | WELL-POSEDNESS | TRAVELING-WAVES | CHEMOTAXIS MODEL | MATHEMATICS | NAVIER-STOKES EQUATIONS | ZERO-VISCOSITY LIMIT | NONLINEAR STABILITY | CONSERVATION-LAWS | HYPERBOLIC-PARABOLIC SYSTEM | DIFFUSION LIMIT | Analysis | Boundary layer

Logarithmic singularity | Energy estimates | Chemotaxis | Boundary layers | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | WELL-POSEDNESS | TRAVELING-WAVES | CHEMOTAXIS MODEL | MATHEMATICS | NAVIER-STOKES EQUATIONS | ZERO-VISCOSITY LIMIT | NONLINEAR STABILITY | CONSERVATION-LAWS | HYPERBOLIC-PARABOLIC SYSTEM | DIFFUSION LIMIT | Analysis | Boundary layer

Journal Article

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