Global classical solutions for mass-conserving, (super)-quadratic reaction-diffusion systems in three and higher space dimensions

DOI10.3934/dcdsb.2016106zbMath1361.35090arXiv1511.04349OpenAlexW2963626721MaRDI QIDQ727921

Takashi Suzuki, Klemens Fellner, Evangelos A. Latos

Publication date: 21 December 2016

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.04349

zbMATH Keywords

entropy methodglobal solutionsclassical solutionsconvergence to equilibriumnonlinear reaction-diffusion systemsmass-conserving system

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Reaction-diffusion equations (35K57) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61)

Related Items (14)

Close-to-equilibrium behaviour of quadratic reaction-diffusion systems with detailed balance ⋮ Explicit exponential convergence to equilibrium for nonlinear reaction-diffusion systems with detailed balance condition ⋮ Trend to Equilibrium for Reaction-Diffusion Systems Arising from Complex Balanced Chemical Reaction Networks ⋮ Close-to-equilibrium regularity for reaction-diffusion systems ⋮ Global regularity and convergence to equilibrium of reaction-diffusion systems with nonlinear diffusion ⋮ Boundedness for reaction–diffusion systems with Lyapunov functions and intermediate sum conditions ⋮ Uniform Boundedness for Reaction-Diffusion Systems with Mass Dissipation ⋮ Asymptotic behavior of solutions to chemical reaction-diffusion systems ⋮ Global renormalized solutions to reaction-cross-diffusion systems with self-diffusion ⋮ Convergence to equilibrium of renormalised solutions to nonlinear chemical reaction-diffusion systems ⋮ Homogenization of degenerate cross-diffusion systems ⋮ Global classical solutions to quadratic systems with mass control in arbitrary dimensions ⋮ Dissipative reaction diffusion systems with quadratic growth ⋮ Solutions of the 4-species quadratic reaction-diffusion system are bounded and \(C^\infty\)-smooth, in any space dimension

Cites Work

• Unnamed Item
• Global-in-time behavior of the solution to a Gierer-Meinhardt system
• Global existence in reaction-diffusion systems with control of mass: a survey
• Global solutions of reaction-diffusion systems
• Entropy methods for reaction-diffusion equations: Slowly growing a-priori bounds
• Quasi-steady-state approximation for a reaction-diffusion system with fast intermediate
• Mathematical methods for hydrodynamic limits
• Weak solutions and supersolutions in \(L^1\) for reaction-diffusion systems
• The diffusion of a population partly driven by its preferences
• On the blow-up of solutions to some semilinear and quasilinear reaction- diffusion systems
• Exponential decay toward equilibrium via entropy methods for reaction-diffusion equations
• Improved Duality Estimates and Applications to Reaction-Diffusion Equations
• Transient and asymptotic dynamics of a prey-predator system with diffusion
• Exponential Convergence to Equilibrium for Nonlinear Reaction-Diffusion Systems Arising in Reversible Chemistry
• Global Regularity of Solutions to Systems of Reaction–Diffusion with Sub-Quadratic Growth in Any Dimension
• Global existence for semilinear parabolic systems.
• Blowup in Reaction-Diffusion Systems with Dissipation of Mass
• Regularity analysis for systems of reaction-diffusion equations
• Global-in-time behavior of Lotka-Volterra system with diffusion
• Global Existence for Quadratic Systems of Reaction-Diffusion
• From reactive Boltzmann equations to reaction-diffusion systems

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