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. RufSecondo
;E. TerraneoUltimo
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.
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