publications
Article
Local well posedness of a 2D semilinear heat equation, |
Ibrahim Slim, Jrad Rym, Majdoub Mohamed, Saanouni Tarek, 2014 |
Bulletin of the Belgian Mathematical Society, 21, 3, 535-551, Mai 2014 |
Résumé
We investigate the initial value problem for a semilinear heat equation
with exponential-growth nonlinearity in two space dimension. First, we
prove the local existence and unconditional uniqueness of solutions in the
Sobolev space H1(R2). The uniqueness part is non trivial although it follows
Brezis-Cazenave’s proof [3] in the case of monomial nonlinearity in dimension
d ≥ 3. Next, we show that in the defocusing case our solution is
bounded, and therefore exists for all time. In the focusing case, we prove
that any solution with negative energy blows up in finite time.
We investigate the initial value problem for a semilinear heat equationwith exponential-growth nonlinearity in two space dimension. First, weprove the local existence and unconditional uniqueness of solutions in theSobolev space H1(R2). The uniqueness part is non trivial although it follows Brezis-Cazenave’s proof [3] in the case of monomial nonlinearity in dimensiond ≥ 3. Next, we show that in the defocusing case our solution i sbounded, and therefore exists for all time. In the focusing case, we provethat any solution with negative energy blows up in finite time.
