Blow-up at space infinity for nonlinear heat equations
نویسنده
چکیده
منابع مشابه
On Blow-up at Space Infinity for Semilinear Heat Equations
We are interested in solutions of semilinear heat equations which blow up at space infinity. In [7], we considered a nonnegative blowing up solution of ut = ∆u+ u, x ∈ R, t > 0 with initial data u0 satisfying 0 ≤ u0(x) ≤ M, u0 ≡ M and lim |x|→∞0 = M, where p > 1 and M > 0 is a constant. We proved in [7] that the solution u blows up exactly at the blow-up time for the spatially constant solution...
متن کاملConvergence and Blow-up of Solutions for a Complex-valued Heat Equation with a Quadratic Nonlinearity
This paper is concerned with the Cauchy problem for a system of parabolic equations which is derived from a complex-valued equation with a quadratic nonlinearity. First we show that if the convex hull of the image of initial data does not intersect the positive real axis, then the solution exists globally in time and converges to the trivial steady state. Next, on the onedimensional space, we p...
متن کاملTransient behavior of solutions to a class of nonlinear boundary value problems
In this paper we consider the asymptotic behavior in time of solutions to the heat equation with certain nonlinear Neumann boundary conditions, ∂u/∂n = F (u). Here F is a function which grows superlinearly. In general solutions exist for only a finite time before “blowing up”, or they decay to zero as time approaches infinity. In both one and two space-dimensions we establish some conditions on...
متن کاملv 1 2 1 Ju n 19 93 Universality in Blow - Up for Nonlinear Heat Equations
We consider the classical problem of the blowing-up of solutions of the nonlinear heat equation. We show that there exist infinitely many profiles around the blow-up point, and for each integer k, we construct a set of codimension 2k in the space of initial data giving rise to solutions that blow-up according to the given profile.
متن کاملTo The Memory of My Father ,
This thesis is concerned with the study of the Blow-up phenomena for parabolic problems, which can be defined in a basic way as the inability to continue the solutions up to or after a finite time, the so called blow-up time. Namely, we consider the blow-up location in space and its rate estimates, for special cases of the following types of problems: (i) Dirichlet problems for semilinear equat...
متن کامل