Existence, Non-existence, and Uniqueness for a Heat Equation with Exponential Nonlinearity in ℝ2

Norisuke Ioku; Bernhard Ruf; Elide Terraneo

doi:10.1007/s11040-015-9199-0

Existence, Non-existence, and Uniqueness for a Heat Equation with Exponential Nonlinearity in ℝ²

Norisuke Ioku, Bernhard Ruf, Elide Terraneo

Research output: Contribution to journal › Article › peer-review

19 Citations (Scopus)

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.

Original language	English
Article number	29
Journal	Mathematical Physics Analysis and Geometry
Volume	18
Issue number	1
DOIs	https://doi.org/10.1007/s11040-015-9199-0
Publication status	Published - 2015 Dec 1
Externally published	Yes

Keywords

Critical nonlinearity
Existence
Heat equation
Non-existence
Uniqueness

ASJC Scopus subject areas

Mathematical Physics
Geometry and Topology

Access to Document

10.1007/s11040-015-9199-0

Cite this

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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.",

keywords = "Critical nonlinearity, Existence, Heat equation, Non-existence, Uniqueness",

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AU - Ruf, Bernhard

AU - Terraneo, Elide

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AB - 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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KW - Existence

KW - Heat equation

KW - Non-existence

KW - Uniqueness

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