The zero number diminishing property under general boundary conditions
The so-called zero number diminishing property (or zero number argument) is a powerful tool in qualitative studies of one dimensional parabolic equations, which says that, under the zero- or non-zero-Dirichlet boundary conditions, the number of zeros of the solution u(x,t) of a linear equation is fi...
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| Published in: | Applied mathematics letters 2019-09, Vol.95, p.41-47 |
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| Main Author: | |
| Format: | Article |
| Language: | eng |
| Subjects: | |
| Online Access: | Get full text |
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| Summary: | The so-called zero number diminishing property (or zero number argument) is a powerful tool in qualitative studies of one dimensional parabolic equations, which says that, under the zero- or non-zero-Dirichlet boundary conditions, the number of zeros of the solution u(x,t) of a linear equation is finite, non-increasing and strictly decreasing when there are multiple zeros (cf. Angenent (1988)). In this paper we extend the result to the problems with more general boundary conditions: u=0 sometime and u≠0 at other times on the domain boundaries. Such results can be applied in particular to parabolic equations with Robin and free boundary conditions. |
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| ISSN: | 0893-9659 1873-5452 |