A heat equation with exponential nonlinearity and with singular initial data in R2
speaker: Bernhard Ruf (Università degli Studi di Milano)abstract: We consider a semilinear heat equation with exponential nonlinearities and with singular initial data in R 2 .
In R n , n ≥ 3, critical growth related to singular initial data is polynomial and
has been studied by several authors. Indeed, existence and non-existence re- sults for singular initial data in suitable L
p -spaces were obtained by Weissler
and Brezis–Cazenave; furthermore, non-uniqueness results for certain singu- lar initial data were given by Ni–Sacks and Terraneo.
In dimension n = 2 critical growth is given by nonlinearities of exponential type (cf. Trudinger–Moser). We prove that similar phenomena as in R n , n ≥ 3, namely existence, non-existence and non-uniqueness, occur for suitable exponential nonlinearities and for singular initial data belonging to certain Orlicz spaces.
timetable:
Fri 13 Sep, 12:10 - 12:45, Aula Dini
<< Go back