Uniform Blow-Up Rates and Asymptotic Estimates of Solutions for Diffusion Systems with Nonlocal Sources

Uniform Blow-Up Rates and Asymptotic Estimates of Solutions for Diffusion Systems with Nonlocal Sources

Global Existence and Blow-Up Solutions and Blow-Up Estimates for Some Evolution Systems with p-Laplacian with Nonlocal Sources

This paper deals with p-Laplacian systems ut − div(|∇u|p−2∇u) = ∫ Ωv α(x, t)dx, x ∈Ω, t > 0, vt − div(|∇v|q−2∇v) = ∫ Ωu β(x, t)dx, x ∈ Ω, t > 0, with null Dirichlet boundary conditions in a smooth bounded domain Ω ⊂ RN , where p,q ≥ 2, α,β ≥ 1. We first get the nonexistence result for related elliptic systems of nonincreasing positive solutions. Secondly by using this nonexistence result, blow ...

On uniform nullcontrollability and blow-up estimates

The paper looks at some of the techniques (separation of variables, Fourier series, Carleman estimates) used to obtain observability and nullcontrollability results to determine qualitatively the asymptotic behavior of the estimates obtained with respect to relevant parameters. We are particularly concerned with blow-up as the control time becomes short (T → 0).

Asymptotic behavior and blow-up of solutions for the viscous diffusion equation

We study the initial–boundary value problem of the viscous diffusion equations which include GBBM equations, Sobolov–Galpern equations and some standard nonlinear diffusion equations as special cases. By using the integral estimate method and the eigenfunction method we prove that when the nonlinear terms satisfy some conditions the solutions of the problem decay to zero according to the expone...

Liouville Theorems, a Priori Estimates, and Blow-up Rates for Solutions of Indefinite Superlinear Parabolic Problems

In this paper we establish new nonlinear Liouville theorems for parabolic problems on half spaces. Based on the Liouville theorems, we derive estimates for the blow-up of positive solutions of indefinite parabolic problems and investigate the complete blow-up of these solutions. We also discuss a priori estimates for indefinite elliptic problems.