Bounded solutions of nonlinear parabolic equations
We are concerned with bounded solutions existing for all times for nonlinear parabolic equations with possibly nonlinear boundary conditions. A counterexample shows that, without an additional condition, a (weak) maximum principle does not hold for linear problems defined on the entire real line...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2010-09-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/conf-proc/19/m2/abstr.html |
| Summary: | We are concerned with bounded solutions existing for all times for nonlinear parabolic equations with possibly nonlinear boundary conditions. A counterexample shows that, without an additional condition, a (weak) maximum principle does not hold for linear problems defined on the entire real line in time. We consider solutions bounded for all times and derive a (weak) maximum principle which is valid on the entire real line. Using comparison techniques, a priori estimates and approximation methods, we prove the existence and, in some cases, positivity and uniqueness of bounded solutions existing for all times. |
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| ISSN: | 1072-6691 |