Blow-up phenomena for a nonlocal semilinear parabolic equation with positive initial energy

Blow-up of a nonlocal semilinear parabolic equation with positive initial energy

Blow up of Solutions with Positive Initial Energy for the Nonlocal Semilinear Heat Equation

In this paper, we investigate a nonlocal semilinear heat equation with homogeneous Dirichlet boundary condition in a bounded domain, and prove that there exist solutions with positive initial energy that blow up in finite time.

Blow-up for a Semilinear Parabolic Equation with Nonlinear Memory and Nonlocal Nonlinear Boundary

where Ω is a bounded domain in RN for N ≥ 1 with C2 boundary ∂Ω, p, q, l and k are positive parameters, the weight function f (x, y) is nonnegative, nontrivial, continuous and defined for x ∈ ∂Ω, y ∈ Ω, while the nonnegative nontrivial initial Received November 14, 2012, accepted January 28, 2013. Communicated by Eiji Yanagida. 2010 Mathematics Subject Classification: 35B35, 35K50, 35K55.

Blow-up analysis for a semilinear parabolic equation with nonlinear memory and nonlocal nonlinear boundary condition

In this paper, we consider a semilinear parabolic equation ut = ∆u + u q ∫ t 0 u(x, s)ds, x ∈ Ω, t > 0 with nonlocal nonlinear boundary condition u|∂Ω×(0,+∞) = ∫ Ω φ(x, y)u (y, t)dy and nonnegative initial data, where p, q ≥ 0 and l > 0. The blow-up criteria and the blow-up rate are obtained.

Existence and Blow-up for a Nonlocal Degenerate Parabolic Equation

In this paper, we establish the local existence and uniqueness of the solution for the degenerate parabolic equation with a nonlocal source and homogeneous Dirichlet boundary condition. Moreover, we prove that the solution blows up in finite time and obtain the blow-up set in some special case. Mathematics Subject Classification: 35K20, 35K30, 35K65