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.
|Journal||Mathematical Physics Analysis and Geometry|
|Publication status||Published - 2015 Dec 1|
- Critical nonlinearity
- Heat equation
ASJC Scopus subject areas
- Mathematical Physics
- Geometry and Topology