# BLOW-UP AND LARGE TIME BEHAVIOR OF SOLUTIONS OF A WEAKLY COUPLED SYSTEM OF REACTION-DIFFUSION EQUATIONS

@article{Umeda2003BLOWUPAL,
title={BLOW-UP AND LARGE TIME BEHAVIOR OF SOLUTIONS OF A WEAKLY COUPLED SYSTEM OF REACTION-DIFFUSION EQUATIONS},
author={Noriaki Umeda},
journal={Tsukuba journal of mathematics},
year={2003},
volume={27},
pages={31-46}
}
• N. Umeda
• Published 1 June 2003
• Physics
• Tsukuba journal of mathematics
where Nb 1, N 1⁄4 f1; 2; . . .Ng, uNþi 1⁄4 ui, uNþi;0 1⁄4 ui0, pNþi 1⁄4 pi ði A N Þ, u 1⁄4 ðu1; u2; . . . ; uNÞ, u0 1⁄4 ðu10; u20; . . . ; uN0Þ, p1⁄4 ðp1; p2; . . . ; pNÞ, db1, pib1 ði AN Þ and QN i1⁄41 pi > 1, ui0 ði A N Þ are nonnegative bounded and continuous functions. Problem (1) has a unique, nonnegative and bounded solution at least locally in time. For given initial values u0, let T 1⁄4 T ðu0Þ be the maximal existence time of the solution. If T 1⁄4 y the solutions are gloval. On the… Expand
14 Citations
Large Time Behavior and Uniqueness of Solutions of a Weakly Coupled System of Reaction-Diffusion Equations
where N ≥ 1, N∗ = {1, 2, . . . N}, d ≥ 1, pi > 0(i ∈ N∗) and ui,0(i ∈ N∗) are nonnegative bounded and continuous functions. Throughout this paper we mean uN+i = ui, uN+i,0 = ui,0, pN+i = pi for eachExpand
Global existence and nonexistence of solutions for a system of nonlinear damped wave equations
Abstract We consider the Cauchy problem for the system of semilinear damped wave equations with small initial data: { ∂ t 2 u 1 − Δ u 1 + ∂ t u 1 = | u k | p 1 , t > 0 , x ∈ R n , ∂ t 2 u 2 − Δ u 2 +Expand
Existence and Nonexistence of Global Solutions in Time for a Reaction-Diffusion System with Inhomogeneous Terms
• Mathematics
• 2008
We consider the initial value problem for the reaction-diffusion system with inhomogeneous terms. In this paper we show the existence and nonexistence of global solution in time. Especially, for theExpand
Global existence and blowup for a coupled parabolic system with time-weighted sources on a general domain
• Physics
• Zeitschrift für angewandte Mathematik und Physik
• 2019
We consider the parabolic problem $$\mathbf{u}_{t}-\Delta \mathbf{u} = F(t, \mathbf{u})$$ut-Δu=F(t,u) in $$\Omega \times (0,T)$$Ω×(0,T) with homogeneous Dirichlet boundary conditions. The nonlinearExpand
Existence of global solutions in time for reaction-diffusion systems with inhomogeneous terms in cones
• Mathematics
• 2012
We consider nonnegative solutions of the initial-boundary value problems in cone domains for the reaction-diffusion systems with inhomogeneous terms dependent on space coordinates and times. In ourExpand
Nonexistence of Global Solutions in Time for Reaction-Diffusion Systems with Inhomogeneous Terms in Cones
• Mathematics
• 2009
We consider initial-boundary value problems for the reaction-diffusion systems with inhomogeneous terms in cones. In this paper we show the nonexistence of global solutions of the problems in time.Expand
Lifespan of Solutions for a Weakly Coupled System of Semilinear Heat Equations
• Mathematics
• Tokyo Journal of Mathematics
• 2020
We introduce a straightforward method to analyze the blow-up of solutions to systems of ordinary differential inequalities, and apply it to study the blow-up of solutions to a weakly coupled systemExpand
Global existence of solutions for a weakly coupled system of semilinear damped wave equations
• Mathematics
• 2015
Abstract In this paper, we consider the Cauchy problem for a weakly coupled system of semilinear damped wave equations. We prove the global existence of solutions for small data in the supercriticalExpand
Critical Fujita curve for a semilinear parabolic system with time-weighted sources
• Mathematics
• 2014
This paper studies the Fujita phenomena for the Cauchy problem to semilinear parabolic equations coupled via the time-weighted sources . The critical curve is determined for a wider range ofExpand
Lifespan estimates for the weakly coupled system of semilinear damped wave equations in the critical case
• Mathematics
• 2020
In this paper, we study lifespan estimates of solution to the Cauchy problem for a weakly coupled system of semilinear damped wave equations in the critical case. By using a suitable test functionExpand