Boundedness and blow-up behavior for reaction–diffusion systems in a bounded domain

DOI10.1016/S0362-546X(97)00706-2zbMath0932.35125MaRDI QIDQ4238365

Jian Zhang

Publication date: 30 March 1999

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

zbMATH Keywords

nonlinear boundary conditionshomogeneous Dirichlet boundary conditions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Reaction-diffusion equations (35K57)

Related Items (8)

Global solutions for quasilinear parabolic systems. ⋮ Global existence and blowup for a reaction-diffusion system with nonlocal boundary condition ⋮ On global existence for semilinear parabolic systems ⋮ Blowup properties for a semilinear reaction-diffusion system with nonlinear nonlocal boundary conditions ⋮ Existence of positive solutions for some nonlinear parabolic systems in exteriors domains ⋮ Blow-up problem of quasilinear weakly coupled reaction-diffusion systems with Neumann boundary conditions ⋮ Global existence and blow-up of solutions for parabolic systems involving cross-diffusion and nonlinear boundary conditions ⋮ Global existence and blow-up for weakly coupled degenerate and singular parabolic equations with nonlocal source

Cites Work

• Unnamed Item
• Unnamed Item
• Non-existence of global solutions to systems of semi-linear parabolic equations
• Quasilinear parabolic systems under nonlinear boundary conditions
• An initial-boundary-value problem for a certain density-dependent diffusion system
• Equilibria and stabilities for competing-species reaction-diffusion equations with Dirichlet boundary data
• On nonlinear reaction-diffusion systems
• A semilinear parabolic system in a bounded domain
• Blow-up estimates of positive solutions of a parabolic system
• Positive steady-state solutions of a competing reaction-diffusion system
• Existence of the global attractor for a strongly coupled parabolic system arising in population dynamics
• Critical blowup and global existence numbers for a weakly coupled system of reaction-diffusion equations
• Blow-up in quasilinear parabolic equations. Transl. from the Russian by Michael Grinfeld
• Smooth solutions to a quasi-linear system of diffusion equations for a certain population model
• Bounded solutions for reaction-diffusion systems with nonlinear boundary conditions
• Stability of Steady States for Prey–Predator Diffusion Equations with Homogeneous Dirichlet Conditions
• On the support properties of solutions for some degenerate quasilinear parabolic systems
• Global solution to some quasilinear parabolic system in population dynamics
• Global solutions for quasilinear parabolic systems with cross-diffusion effects
• Local existence of general nonlinear parabolic systems
• Blow-up vs. global existence for a semilinear reaction-diffusion system in a bounded domain

This page was built for publication: Boundedness and blow-up behavior for reaction–diffusion systems in a bounded domain