Complete blow-up after Tmax for the solution of a semilinear heat equation

Complete Blow-Up after T,,, for the Solution of a 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...

Existence and blow-up of solution of Cauchy problem for the sixth order damped Boussinesq equation

‎In this paper‎, ‎we consider the existence and uniqueness of the global solution for the sixth-order damped Boussinesq equation‎. ‎Moreover‎, ‎the finite-time blow-up of the solution for the equation is investigated by the concavity method‎.

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.

Asymptotic Behaviour and Blow-up of Some Unbounded Solutions for a Semilinear Heat Equation

The initial-boundary value problem for the nonlinear heat equation u, = Au + Xf(u) might possibly have global classical unbounded solutions, u* = u(x, r; uS), for some "critical" initial data u*. The asymptotic behaviour of such solutions is studied, when there exists a unique bounded steady state w(x,A) for some values of L We find, for radial symmetric solutions, that u*(r,t)-*w{r) for any 0 ...