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
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