We consider a semilinear heat equation with exponential nonlinearity in ℝ2. We prove that local solutions do not exist for certain data in the Orlicz space exp L2(ℝ2), even though a small data global existence result holds in the same space exp L2(ℝ2). Moreover, some suitable subclass of exp L2(ℝ2) for local existence and uniqueness is proposed.

Existence, non-existence, and uniqueness for a heat equation with exponential nonlinearity in R^2 / N. Ioku, B. Ruf, E. Terraneo. - In: MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY. - ISSN 1385-0172. - 18:1(2015 Dec), pp. 29.1-29.19. [10.1007/s11040-015-9199-0]

Existence, non-existence, and uniqueness for a heat equation with exponential nonlinearity in R^2

B. Ruf
Secondo
;
E. Terraneo
Ultimo
2015

Abstract

We consider a semilinear heat equation with exponential nonlinearity in ℝ2. We prove that local solutions do not exist for certain data in the Orlicz space exp L2(ℝ2), even though a small data global existence result holds in the same space exp L2(ℝ2). Moreover, some suitable subclass of exp L2(ℝ2) for local existence and uniqueness is proposed.
heat equation; existence; non-existence; uniqueness; critical nonlinearity
Settore MAT/05 - Analisi Matematica
21-ott-2015
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/387074
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