Sixth Mississippi State Conference on Differential Equations and
Computational Simulations.
Electron. J. Diff. Eqns., Conference 15 (2007), pp. 51-65.
Existence and non-existence results for a nonlinear heat equation
Canan Celik
Abstract:
In this study, we consider the
nonlinear heat equation

with Dirichlet and mixed boundary conditions, where
is a smooth bounded domain
and
is the critical exponent.
For an initial condition
,
we prove the non-existence
of local solution in
for
the mixed boundary condition. Our proof is based on comparison
principle for Dirichlet and mixed boundary value problems. We also
establish the global existence in
to the Dirichlet
problem, for any fixed
with
sufficiently small.
Published February 28, 2007.
Math Subject Classifications: 35K55, 35K05, 35K57, 35B33.
Key Words: Nonlinear heat equation; mixed boundary condition;
global existence; critical exponent.
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Canan Celik
Departmane to Mathematics
TOBB Economics and Technology University
Sögütözü cad. No. 43. 06560 Sögütözü
Ankara, Turkey
email: canan.celik@etu.edu.tr |
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