1.
Full Text
Global existence of solutions of the simplified Ericksen–Leslie system in dimension two

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 1/2011, Volume 40, Issue 1, pp. 15 - 36

In the 1960s, Ericksen and Leslie established the hydrodynamic theory for modelling liquid crystal flow. In this paper, we investigate a simplified model of...

Calculus of Variations and Optimal Control; Optimization | Systems Theory, Control | Theoretical, Mathematical and Computational Physics | Analysis | Mathematics | 35K45 | 35K55 | MATHEMATICS | MATHEMATICS, APPLIED | NAVIER-STOKES EQUATIONS | HARMONIC-MAPPINGS | LIQUID-CRYSTALS | FLOW | PARTIAL REGULARITY | SURFACES | Mathematics Subject Classification : 35K45, 35K55

Calculus of Variations and Optimal Control; Optimization | Systems Theory, Control | Theoretical, Mathematical and Computational Physics | Analysis | Mathematics | 35K45 | 35K55 | MATHEMATICS | MATHEMATICS, APPLIED | NAVIER-STOKES EQUATIONS | HARMONIC-MAPPINGS | LIQUID-CRYSTALS | FLOW | PARTIAL REGULARITY | SURFACES | Mathematics Subject Classification : 35K45, 35K55

Journal Article

Mathematische Annalen, ISSN 0025-5831, 12/2015, Volume 363, Issue 3, pp. 1117 - 1145

We consider the maximal regularity problem for non-autonomous evolution equations 1 Each operator $$A(t)$$ A ( t ) is associated with a sesquilinear form...

47D06 | Mathematics, general | Mathematics | 35K50 | 35K45 | 35K90 | MATHEMATICS | PARABOLIC EQUATIONS | PSEUDODIFFERENTIAL-OPERATORS

47D06 | Mathematics, general | Mathematics | 35K50 | 35K45 | 35K90 | MATHEMATICS | PARABOLIC EQUATIONS | PSEUDODIFFERENTIAL-OPERATORS

Journal Article

Proceedings of the London Mathematical Society, ISSN 0024-6115, 11/2019, Volume 119, Issue 5, pp. 1279 - 1335

This paper is concerned with some spreading properties of monostable Lotka–Volterra two‐species competition‐diffusion systems when the initial values are null...

92D25 (primary) | 35K57 | 35K45 | Analysis of PDEs | Mathematics

92D25 (primary) | 35K57 | 35K45 | Analysis of PDEs | Mathematics

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 06/2014, Volume 256, Issue 12, pp. 3912 - 3942

In this paper we introduce a purely variational approach to time dependent problems, yielding the existence of global parabolic minimizers, that...

Parabolic minimizers | Parabolic systems | Evolutionary solutions via calculus of variations | Evolutionary variational solutions | Existence | 35D05 | 49J40 | 35A01 | 35K45 | 35K87 | PARABOLIC EQUATIONS | METRIC-SPACES | PRINCIPLE | GRADIENT FLOWS | CONJECTURE | MATHEMATICS | ENERGY-DISSIPATION FUNCTIONALS | GIORGI | GROWTH | SYSTEMS

Parabolic minimizers | Parabolic systems | Evolutionary solutions via calculus of variations | Evolutionary variational solutions | Existence | 35D05 | 49J40 | 35A01 | 35K45 | 35K87 | PARABOLIC EQUATIONS | METRIC-SPACES | PRINCIPLE | GRADIENT FLOWS | CONJECTURE | MATHEMATICS | ENERGY-DISSIPATION FUNCTIONALS | GIORGI | GROWTH | SYSTEMS

Journal Article

Journal of Nonlinear Science, ISSN 0938-8974, 10/2011, Volume 21, Issue 5, pp. 747 - 783

Much has been studied on the spreading speed and traveling wave solutions for cooperative reaction–diffusion systems. In this paper, we shall establish the...

Theoretical, Mathematical and Computational Physics | Traveling waves | Mathematics | 35K57 | 35K45 | Reaction–diffusion systems | 92D25 | Analysis | Non-cooperative systems | Appl.Mathematics/Computational Methods of Engineering | Mechanics | Economic Theory | 35B40 | Spreading speed | 92D40 | Reaction-diffusion systems | MATHEMATICS, APPLIED | LINEAR DETERMINACY | THEOREM | EQUATIONS | RECURSIONS | PHYSICS, MATHEMATICAL | FRONTS | MECHANICS | MODELS | GROWTH

Theoretical, Mathematical and Computational Physics | Traveling waves | Mathematics | 35K57 | 35K45 | Reaction–diffusion systems | 92D25 | Analysis | Non-cooperative systems | Appl.Mathematics/Computational Methods of Engineering | Mechanics | Economic Theory | 35B40 | Spreading speed | 92D40 | Reaction-diffusion systems | MATHEMATICS, APPLIED | LINEAR DETERMINACY | THEOREM | EQUATIONS | RECURSIONS | PHYSICS, MATHEMATICAL | FRONTS | MECHANICS | MODELS | GROWTH

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 04/2019, Volume 292, Issue 4, pp. 724 - 732

In this paper we consider a one‐dimensional fully parabolic quasilinear Keller–Segel system with critical nonlinear diffusion. We show uniform‐in‐time...

boundedness of solutions | 92C17 | Lyapunov‐like functional | 35K45 | 35B45 | chemotaxis | Lyapunov-like functional | MATHEMATICS

boundedness of solutions | 92C17 | Lyapunov‐like functional | 35K45 | 35B45 | chemotaxis | Lyapunov-like functional | MATHEMATICS

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 7/2016, Volume 107, Issue 1, pp. 43 - 57

We consider a linear non-autonomous evolutionary Cauchy problem 0.1 $$\begin{aligned}\dot{u}(t)+{\mathcal{A}}(t)u(t)=f(t) \quad { for } \; {a.e. t} \in...

47D06 | 35K50 | Approximation | Sesquilinear forms | 35K90 | Maximal regularity | Mathematics, general | Mathematics | Non-autonomous evolution equations | 35K45 | MATHEMATICS

47D06 | 35K50 | Approximation | Sesquilinear forms | 35K90 | Maximal regularity | Mathematics, general | Mathematics | Non-autonomous evolution equations | 35K45 | MATHEMATICS

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 05/2018, Volume 41, Issue 8, pp. 3138 - 3154

This paper considers the 2‐species chemotaxis‐Stokes system with competitive kinetics...

asymptotic stability | global existence | chemotaxis‐Stokes | chemotaxis-Stokes | MATHEMATICS, APPLIED | STABILIZATION | STABILITY | SENSITIVITY | BOUNDEDNESS | MODEL | CHEMICAL DIFFUSION | KELLER-SEGEL SYSTEM | LOGISTIC SOURCE | FLUID | CHEMOATTRACTANT | Animal behavior | Nonlinear equations | Computational fluid dynamics | Stokes law (fluid mechanics) | Smooth boundaries | Mathematics - Analysis of PDEs

asymptotic stability | global existence | chemotaxis‐Stokes | chemotaxis-Stokes | MATHEMATICS, APPLIED | STABILIZATION | STABILITY | SENSITIVITY | BOUNDEDNESS | MODEL | CHEMICAL DIFFUSION | KELLER-SEGEL SYSTEM | LOGISTIC SOURCE | FLUID | CHEMOATTRACTANT | Animal behavior | Nonlinear equations | Computational fluid dynamics | Stokes law (fluid mechanics) | Smooth boundaries | Mathematics - Analysis of PDEs

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 04/2018, Volume 21, Issue 2, pp. 276 - 311

We discuss an initial-boundary value problem for a fractional diffusion equation with Caputo time-fractional derivative where the coefficients are dependent on...

weak solution | Primary 35R11 | initial-boundary value problem | regularity | fractional diffusion equation | Secondary 35K45, 26A33, 34A08 | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SPACES | WEAK SOLUTIONS | Time dependence | Dirichlet problem | Boundary value problems

weak solution | Primary 35R11 | initial-boundary value problem | regularity | fractional diffusion equation | Secondary 35K45, 26A33, 34A08 | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SPACES | WEAK SOLUTIONS | Time dependence | Dirichlet problem | Boundary value problems

Journal Article

Journal of Mathematical Biology, ISSN 0303-6812, 5/2016, Volume 72, Issue 6, pp. 1429 - 1439

In this short paper, we establish a priori $$L^\infty $$ L ∞ -norm estimates for solutions of a class of reaction-diffusion systems which can be used to model...

92D30 | Reaction-diffusion system | A priori $$L^\infty $$ L ∞ -norm estimate | Epidemic models | Mathematical and Computational Biology | 35B45 | Mathematics | Applications of Mathematics | 35K45

92D30 | Reaction-diffusion system | A priori $$L^\infty $$ L ∞ -norm estimate | Epidemic models | Mathematical and Computational Biology | 35B45 | Mathematics | Applications of Mathematics | 35K45

Journal Article

Journal of Evolution Equations, ISSN 1424-3199, 6/2018, Volume 18, Issue 2, pp. 755 - 775

We study the large time behavior of a class of diffusive predator–prey systems posed on the whole Euclidean space. By studying a family of similar problems...

Persistence | Predator–prey system | Analysis | Asymptotic behavior | Mathematics | 35K57 | 35K45 | 35K55 | MATHEMATICS | MATHEMATICS, APPLIED | Predator-prey system

Persistence | Predator–prey system | Analysis | Asymptotic behavior | Mathematics | 35K57 | 35K45 | 35K55 | MATHEMATICS | MATHEMATICS, APPLIED | Predator-prey system

Journal Article

Osaka Journal of Mathematics, ISSN 0030-6126, 06/2012, Volume 49, Issue 2, pp. 331 - 348

Consider the Cauchy problem for a system of weakly coupled heat equations, whose typical one is {u(t) - Delta u = vertical bar v vertical bar(p-1)v, v(t) -...

MATHEMATICS | CAUCHY-PROBLEM | NONEXISTENCE | BLOW-UP | GLOBAL EXISTENCE | 35K45 | 35B40

MATHEMATICS | CAUCHY-PROBLEM | NONEXISTENCE | BLOW-UP | GLOBAL EXISTENCE | 35K45 | 35B40

Journal Article

Stochastic Partial Differential Equations: Analysis and Computations, ISSN 2194-0401, 3/2015, Volume 3, Issue 1, pp. 52 - 83

Systems of parabolic, possibly degenerate parabolic SPDEs are considered. Existence and uniqueness are established in Sobolev spaces. Similar results are...

Computational Mathematics and Numerical Analysis | 35F40 | Probability Theory and Stochastic Processes | Statistical Theory and Methods | Mathematics | Computational Science and Engineering | 35K45 | Cauchy problem | 35K65 | First order symmetric hyperbolic system | Numerical Analysis | 60H15 | Partial Differential Equations | Degenerate stochastic parabolic PDEs | Mathematics - Analysis of PDEs

Computational Mathematics and Numerical Analysis | 35F40 | Probability Theory and Stochastic Processes | Statistical Theory and Methods | Mathematics | Computational Science and Engineering | 35K45 | Cauchy problem | 35K65 | First order symmetric hyperbolic system | Numerical Analysis | 60H15 | Partial Differential Equations | Degenerate stochastic parabolic PDEs | Mathematics - Analysis of PDEs

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 9/2018, Volume 178, Issue 3, pp. 950 - 972

The behavior of a fishing fleet and its impact onto the biomass of fish can be described by a nonlinear parabolic diffusion–reaction equation. Looking for an...

35K20 | Non-convex optimization | Fishing strategies | Mathematics | Theory of Computation | 35K57 | 35K45 | Optimization | 49K20 | Calculus of Variations and Optimal Control; Optimization | 49K40 | Operations Research/Decision Theory | Optimal control | 65M60 | Applications of Mathematics | Engineering, general | OPTIMAL-HARVESTING PROBLEM | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PARABOLIC EQUATIONS | MODEL | MEASURE-VALUED SOLUTIONS | RENEWABLE RESOURCE | Algorithms | Fishing | Animal behavior | Mathematical optimization | Finite element method | Well posed problems

35K20 | Non-convex optimization | Fishing strategies | Mathematics | Theory of Computation | 35K57 | 35K45 | Optimization | 49K20 | Calculus of Variations and Optimal Control; Optimization | 49K40 | Operations Research/Decision Theory | Optimal control | 65M60 | Applications of Mathematics | Engineering, general | OPTIMAL-HARVESTING PROBLEM | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PARABOLIC EQUATIONS | MODEL | MEASURE-VALUED SOLUTIONS | RENEWABLE RESOURCE | Algorithms | Fishing | Animal behavior | Mathematical optimization | Finite element method | Well posed problems

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 7/2015, Volume 105, Issue 1, pp. 79 - 91

We consider the maximal regularity problem for non-autonomous evolution equations 0.1 $$\begin{array}{l}{u'(t) + A(t)\,u(t) = f(t), \quad t \in (0, \tau]}\\...

47D06 | 35K50 | Sesquilinear forms | 35K90 | Maximal regularity | Mathematics, general | Mathematics | Non-autonomous evolution equations | 35K45 | Differential operators with boundary conditions | MATHEMATICS | Bisphenol-A | Analysis of PDEs

47D06 | 35K50 | Sesquilinear forms | 35K90 | Maximal regularity | Mathematics, general | Mathematics | Non-autonomous evolution equations | 35K45 | Differential operators with boundary conditions | MATHEMATICS | Bisphenol-A | Analysis of PDEs

Journal Article

Journal of Evolution Equations, ISSN 1424-3199, 9/2017, Volume 17, Issue 3, pp. 883 - 907

We consider non-autonomous evolutionary problems of the form $$u' (t)+A(t)u(t) = f(t), \quad u(0) = u_{0},$$ u ′ ( t ) + A ( t ) u ( t ) = f ( t ) , u ( 0 ) =...

47D06 | 35K50 | Analysis | Sesquilinear forms | 35K90 | Maximal regularity | Mathematics | Non-autonomous evolution equations | 35K45 | FORMS | MATHEMATICS | MATHEMATICS, APPLIED | BESOV | EVOLUTION-EQUATIONS | L-P | SOBOLEV

47D06 | 35K50 | Analysis | Sesquilinear forms | 35K90 | Maximal regularity | Mathematics | Non-autonomous evolution equations | 35K45 | FORMS | MATHEMATICS | MATHEMATICS, APPLIED | BESOV | EVOLUTION-EQUATIONS | L-P | SOBOLEV

Journal Article

Ricerche di Matematica, ISSN 0035-5038, 6/2019, Volume 68, Issue 1, pp. 295 - 314

A predator–prey system involving cross-diffusion is obtained at the formal level as a singular limit of a four-species reaction–diffusion system, following the...

Cross-diffusion equations | 35B25 | 35B36 | Turing patterns | Functional responses | Probability Theory and Stochastic Processes | Mathematics | 35K57 | 35K45 | 35Q92 | Geometry | Predator–prey equations | Algebra | 92D25 | Turing instability | Analysis | Numerical Analysis | Mathematics, general | MATHEMATICS | MATHEMATICS, APPLIED | Predator-prey equations | MUTUAL INTERFERENCE

Cross-diffusion equations | 35B25 | 35B36 | Turing patterns | Functional responses | Probability Theory and Stochastic Processes | Mathematics | 35K57 | 35K45 | 35Q92 | Geometry | Predator–prey equations | Algebra | 92D25 | Turing instability | Analysis | Numerical Analysis | Mathematics, general | MATHEMATICS | MATHEMATICS, APPLIED | Predator-prey equations | MUTUAL INTERFERENCE

Journal Article

Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 6/2018, Volume 25, Issue 3, pp. 1 - 39

We consider in this paper a microscopic model (that is, a system of three reaction–diffusion equations) incorporating the dynamics of handling and searching...

Cross-diffusion equations | 35B25 | 35B36 | Turing patterns | Mathematics | 35K57 | 35K45 | 35Q92 | Predator–prey equations | 92D25 | Turing instability | Analysis | functional responses | DERIVATION | EXISTENCE | MATHEMATICS, APPLIED | EQUATIONS | MUTUAL INTERFERENCE | PATTERN-FORMATION | FAST REACTION LIMIT | CROSS-DIFFUSION | DISCRETE | DYNAMICS | Predator-prey equations

Cross-diffusion equations | 35B25 | 35B36 | Turing patterns | Mathematics | 35K57 | 35K45 | 35Q92 | Predator–prey equations | 92D25 | Turing instability | Analysis | functional responses | DERIVATION | EXISTENCE | MATHEMATICS, APPLIED | EQUATIONS | MUTUAL INTERFERENCE | PATTERN-FORMATION | FAST REACTION LIMIT | CROSS-DIFFUSION | DISCRETE | DYNAMICS | Predator-prey equations

Journal Article

Numerische Mathematik, ISSN 0029-599X, 7/2015, Volume 130, Issue 3, pp. 541 - 566

We consider a two-dimensional model of double-diffusive convection and its time discretisation using a second-order scheme (based on backward differentiation...

Mathematical Methods in Physics | 35B35 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Numerical and Computational Physics | Mathematics, general | Mathematics | 65M12 | 35K45 | ATTRACTORS | MATHEMATICS, APPLIED | APPROXIMATION | BOUNDS

Mathematical Methods in Physics | 35B35 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Numerical and Computational Physics | Mathematics, general | Mathematics | 65M12 | 35K45 | ATTRACTORS | MATHEMATICS, APPLIED | APPROXIMATION | BOUNDS

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 7/2013, Volume 47, Issue 3, pp. 611 - 665

We consider compact convex hypersurfaces contracting by functions of their curvature. Under the mean curvature flow, uniformly convex smooth initial...

Primary 35K55 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | 58J35 | 35K45 | MATHEMATICS | MATHEMATICS, APPLIED | MAXIMUM PRINCIPLE | MOTION | PARABOLIC EQUATIONS | ROOT | MEAN-CURVATURE | GAUSS CURVATURE | ELLIPTIC-EQUATIONS | FLOW | UNIQUENESS | Research institutes | Discs | Mathematical analysis | Segments | Ridges | Curvature | Contracts | Contraction | Constraining

Primary 35K55 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | 58J35 | 35K45 | MATHEMATICS | MATHEMATICS, APPLIED | MAXIMUM PRINCIPLE | MOTION | PARABOLIC EQUATIONS | ROOT | MEAN-CURVATURE | GAUSS CURVATURE | ELLIPTIC-EQUATIONS | FLOW | UNIQUENESS | Research institutes | Discs | Mathematical analysis | Segments | Ridges | Curvature | Contracts | Contraction | Constraining

Journal Article

No results were found for your search.

Cannot display more than 1000 results, please narrow the terms of your search.