From Nonlocal to Classical Shigesada--Kawasaki--Teramoto Systems: Triangular Case with Bounded Coefficients
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Publication:5208765
DOI10.1137/19M1243294zbMath1428.35156arXiv1711.08662OpenAlexW2999137015WikidataQ126402813 ScholiaQ126402813MaRDI QIDQ5208765
Publication date: 10 January 2020
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1711.08662
PDEs in connection with biology, chemistry and other natural sciences (35Q92) Weak solutions to PDEs (35D30) Second-order parabolic systems (35K40)
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Cites Work
- Unnamed Item
- Unnamed Item
- On triangular reaction cross-diffusion systems with possible self-diffusion
- Density of smooth functions in weighted Sobolev spaces
- A relation between cross-diffusion and reaction-diffusion
- Rigorous passage to the limit in a system of reaction-diffusion equations towards a system including cross diffusions
- Dynamic theory of quasilinear parabolic equations. II: Reaction-diffusion systems
- Diffusion, cross-diffusion and competitive interaction
- Conservative cross diffusions and pattern formation through relaxation
- The spatial homogeneity of stable equilibria of some reaction-diffusion systems on convex domains
- Spatial segregation in competitive interaction-diffusion equations
- On the global existence of a cross-diffusion system
- A note on the uniqueness of weak solutions to a class of cross-diffusion systems
- Global existence analysis of cross-diffusion population systems for multiple species
- About the entropic structure of detailed balanced multi-species cross-diffusion equations
- Propagation speed of travelling fronts in non local reaction-diffusion equations
- Diffusion, self-diffusion and cross-diffusion
- Semi-discretization in time and numerical convergence of solutions of a nonlinear cross-diffusion population model
- Non local Lotka-Volterra system with cross-diffusion in an heterogeneous medium
- Cross-diffusion systems and fast-reaction limits
- New results for triangular reaction cross diffusion system
- Entropic structure and duality for multiple species cross-diffusion systems
- Analysis of a parabolic cross-diffusion population model without self-diffusion
- The global existence of solutions for a cross-diffusion system
- Reaction-diffusion system approximation to the cross-diffusion competition system
- Sul problema di Cauchy-Dirichlet per equationi paraboliche del secondo ordine, non variazionali, a coefficienti discontinui
- Improved Duality Estimates and Applications to Reaction-Diffusion Equations
- Global Well-Posedness of a Conservative Relaxed Cross Diffusion System
- On the Entropic Structure of Reaction-Cross Diffusion Systems
- Global Existence and Uniform Boundedness of Smooth Solutions to a Cross-Diffusion System with Equal Diffusion Rates
- Pattern and Waves for a Model in Population Dynamics with Nonlocal Consumption of Resources
- The non-local Fisher–KPP equation: travelling waves and steady states
- Dynamic theory of quasilinear parabolic equations—I. Abstract evolution equations
- Weighted Sobolev spaces
- Global solution to some quasilinear parabolic system in population dynamics
- Blowup in Reaction-Diffusion Systems with Dissipation Of Mass
- Analysis of a Multidimensional Parabolic Population Model with Strong Cross-Diffusion
- Global existence for a class of triangular parabolic systems on domains of arbitrary dimension
- Gradient Estimates and Global Existence of Smooth Solutions to a Cross-Diffusion System
- Everywhere Regularity of Solutions to a Class of Strongly Coupled Degenerate Parabolic Systems
- Entropy, Duality, and Cross Diffusion
- Weighted Norm Inequalities for the Hardy Maximal Function
