Blow-up Rate Estimates and Blow-up Set for a System of Two Heat Equations with Coupled Nonlinear Neumann Boundary Conditions

The Blow-up Rate Estimates for a System of Heat Equations with Nonlinear Boundary Conditions

This paper deals with the blow-up properties of positive solutions to a system of two heat equations ut = ∆u, vt = ∆v in BR× (0, T ) with Neumann boundary conditions ∂u ∂η = e vp , ∂v ∂η = e uq on ∂BR × (0, T ), where p, q > 1, BR is a ball in Rn, η is the outward normal. The upper bounds of blow-up rate estimates were obtained. It is also proved that the blow-up occurs only on the boundary.

Blow-up in Nonlinear Heat Equations

In this paper we study the blowup problem of nonlinear heat equations. Our result show that for a certain family of initial conditions the solution will blowup in finite time, the blowup parameters satisfy some dynamics which are asymptotic stable, moreover we provide the remainder estimates. Compare to the previous works our approach is analogous to one used in bifurcation theory and our techn...

Blow-Up Time for Nonlinear Heat Equations with Transcendental Nonlinearity

where x ∈ R, F is a given nonlinear function and u is unknown. Due to the mathematical and physical importance, existence and uniqueness theories of solutions of nonlinear heat equations have been extensively studied by many mathematicians and physicists, for example, 1–10 and references therein. Unlike other studies, we focus on the nonlinear heat equations with transcendental nonlinearities s...

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...

Blow-up at space infinity for nonlinear heat equations