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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
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
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
Journal Article
Communications in Mathematical Sciences, ISSN 1539-6746, 2017, Volume 15, Issue 4, pp. 1073 - 1106
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
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
Journal Article
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
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2020, Volume 268, Issue 4, pp. 1379 - 1411
Journal Article
Mathematical Biosciences, ISSN 0025-5564, 12/2012, Volume 240, Issue 2, pp. 161 - 168
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
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
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
Journal Article
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