A mass-lumping finite element method for radially symmetric solution of a multidimensional semilinear heat equation with blow-up

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...

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

Blow-up of Solutions of a Semilinear Heat Equation with a Memory Term

where u is the temperature, d is the diffusion coefficient, and the integral term represents the memory effect in the material. The study of this type of equations has drawn a considerable attention, see [3, 4, 10, 12, 13]. From a mathematical point of view, one would expect the integral term to be dominated by the leading term in the equation. Therefore, the theory of parabolic equations appli...

Blow-up of Solutions of a Semilinear Heat Equation with a Visco-elastic Term

In this work we consider an initial boundary value problem related to the equation ut −∆u+ ∫ t 0 g(t− s)∆u(x, s)ds = |u|p−2u and prove, under suitable conditions on g and p, a blow-up result for solutions with negative or vanishing initial energy. This result improves an earlier one by the author. Mathematics Subject Classification (2000). 35K05 35K65.

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.