Existence and nonexistence of solutions for the heat equation with a superlinear source term

Yohei Fujishima; Norisuke Ioku

doi:10.1016/j.matpur.2018.08.001

Existence and nonexistence of solutions for the heat equation with a superlinear source term

Yohei Fujishima, Norisuke Ioku

Research output: Contribution to journal › Article

6 Citations (Scopus)

Abstract

We develop a classification theory for the existence and non-existence of local in time solutions for initial value problems for nonlinear heat equations. By focusing on some quasi-scaling property and its invariant integral, we reveal the explicit threshold integrability of initial data that classifies the existence and nonexistence of solutions. Typical nonlinear terms, for instance polynomial type, exponential type and their sums, products and compositions can be treated as applications.

Original language	English
Pages (from-to)	128-158
Number of pages	31
Journal	Journal des Mathematiques Pures et Appliquees
Volume	118
DOIs	https://doi.org/10.1016/j.matpur.2018.08.001
Publication status	Published - 2018 Oct
Externally published	Yes

Keywords

Existence and nonexistence
Nonlinear heat equation
Scale invariance
Singular initial data

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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Fujishima, Y., & Ioku, N. (2018). Existence and nonexistence of solutions for the heat equation with a superlinear source term. Journal des Mathematiques Pures et Appliquees, 118, 128-158. https://doi.org/10.1016/j.matpur.2018.08.001

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KW - Singular initial data

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