Blow-up in nonlinear heat equations

Blow-up in Nonlinear Heat Equations

In this paper we study the blowup problem of nonlinear heat equations. Our result show that for a certain family of initial conditions the solution will blowup in finite time, the blowup parameters satisfy some dynamics which are asymptotic stable, moreover we provide the remainder estimates. Compare to the previous works our approach is analogous to one used in bifurcation theory and our techn...

Blow-up at space infinity for nonlinear heat equations

Blow-Up Time for Nonlinear Heat Equations with Transcendental Nonlinearity

where x ∈ R, F is a given nonlinear function and u is unknown. Due to the mathematical and physical importance, existence and uniqueness theories of solutions of nonlinear heat equations have been extensively studied by many mathematicians and physicists, for example, 1–10 and references therein. Unlike other studies, we focus on the nonlinear heat equations with transcendental nonlinearities s...

v 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.

Blow-up in Nonlinear Heat Equations from the Dynamical Systems Point of View