Behavior Rigidity Near Non-Isolated Blow-up Points for the Semilinear Heat Equation

Initial blow-up solution of a semilinear heat equation

We study the existence and uniqueness of a maximal solution of equation ut − ∆u + f(u) = 0 in Ω× (0,∞), where Ω is a domain with a non-empty compact boundary, which satisfies u = g on ∂Ω × (0,∞), assuming that g and f are given continuous functions and f is also convex, nondecreasing, f(0) = 0 and verifies Keller-Osserman condition. We show that if the boundary of Ω satisfies the parabolic Wien...

Blow up for the Semilinear Wave Equation in Schwarzschild Metric

We study the semilinear wave equation in Schwarzschild metric (3 + 1 dimensional space time). First, we establish that the problem is locally well posed in H for any σ > 1; then we prove the blow up of the solution for every p > 1 and non negative initial data. The work is dedicated to prof. Yvonne Choquet Bruhat in occasion of her 80th year.

Complete Blow-Up after T,,, for the Solution of a Semilinear Heat Equation

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 Points of Solution Curves for a Semilinear Problem

We study a semilinear elliptic equation with an asymptotic linear nonlinearity. Exact multiplicity of solutions are obtained under various conditions on the nonlinearity and the spectrum set. Our method combines a bifurcation approach and Leray–Schauder degree theory.