Pointwise and L2 bounds in some nonstandard problems for the heat equation |
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| Authors: | L.E. Payne |
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| Affiliation: | a Department of Mathematics, Cornell University, Ithaca, NY 14853, USA
b Department of Mathematics, University of Tennessee, Knoxville, TN 37916, USA |
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| Abstract: | We consider some initial-boundary value problems for the linear and nonlinear heat equation where the gradient of the solution is prescribed on the boundary. Assuming that a solution exists, we obtain bounds for the solution and its gradient by maximum principle arguments or by means of differential and integral inequalities. |
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| Keywords: | Heat equation Nonstandard problems Pointwise bounds |
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