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

By Y. Fujishima, Norisuke Ioku. Journal des Mathématiques Pures et Appliquées, 2016

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Classification theory on the existence and non-existence of local in time solutions for initial value problems of nonlinear heat equations are investigated. Without assuming a concrete growth rate on a nonlinear term, we reveal the threshold integrability of initial data which classify existence and nonexistence of solutions via a quasi-scaling and its invariant integral. Typical nonlinear terms, for instance polynomial type, exponential type and its sum, product and composition, can be treated as applications.

Subfields: Applied Mathematics, Mathematical Physics

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