A semilinear parabolic system with coupling variable exponents

Critical Exponents for a Semilinear Parabolic Equation with Variable Reaction

In this paper we study the blow-up phenomenon for nonnegative solutions to the following parabolic problem: ut(x, t) = ∆u(x, t) + (u(x, t)) , in Ω× (0, T ), where 0 < p− = min p ≤ p(x) ≤ max p = p+ is a smooth bounded function. After discussing existence and uniqueness we characterize the critical exponents for this problem. We prove that there are solutions with blow-up in finite time if and o...

Blow-up for Parabolic and Hyperbolic Problems with Variable Exponents

In this paper we study the blow up problem for positive solutions of parabolic and hyperbolic problems with reaction terms of local and nonlocal type involving a variable exponent. We prove the existence of initial data such that the corresponding solutions blow up at a finite time.

Blowup Rate Estimate for a System of Semilinear Parabolic Equations

In this paper, we study the blowup rate estimate for a system of semilinear parabolic equations. The blowup rate depends on whether the two components of the solution of this system blow up simultaneously or not.

Blow-up estimates for a semilinear coupled parabolic system

This work deals with a semilinear parabolic systemwhich is coupled both in the equations and in the boundary conditions. The blow-up phenomena of its positive solutions are studied using the scaling method, the Green function and Schauder estimates. The upper and lower bounds of blow-up rates are then obtained. Moreover we show the influences of the reaction terms and the boundary absorption te...

Semilinear parabolic problems