| Abstract: |
| We consider a semilinear heat equation with exponential nonlinearities and singular data in $R^2$.
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In $R^N$, $N \ge 3$, critical growth related to singular initial data is polynomial and has been studied by several authors.
Existence and non-existence results for singular initial data in suitable $ L^p$-spaces were obtained by F. Weissler and H. Brezis - T. Cazenave; furthermore, non-uniqueness results for certain singular initial data were given by W.-M. Ni - P. Sacks and E. Terraneo.
In $N = 2$ critical growth is given by nonlinearities of exponential type (cf. N.~Trudinger - J.~Moser).
With prove that similar phenomena, namely existence, non-existence and non-uniqueness, occur for suitable exponential nonlinearities and
singular initial data in certain Orlicz spaces. |
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