Localization and blow-up of thermal waves in nonlinear heat conduction with peaking

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 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...

A blow-up result for nonlinear generalized heat equation

Available online xxxx Keywords: Nonlinear heat equation Blow up Sobolev spaces with variable exponents a b s t r a c t In this paper we consider a nonlinear heat equation with nonlinearities of variable-exponent type. We show that any solution with nontrivial initial datum blows up in finite time. We also give a two-dimension numerical example to illustrate our result.

Blow-up at space infinity for nonlinear heat equations

Existence and Blow up of Small-amplitude Nonlinear Waves with a Sign-changing Potential

We study the nonlinear wave equation with a sign-changing potential in any space dimension. If the potential is small and rapidly decaying, then the existence of smallamplitude solutions is driven by the nonlinear term. If the potential induces growth in the linearized problem, however, solutions that start out small may blow-up in finite time.