Chipot, M; Quittner, P (2004). Equilibria, connecting orbits and a priori bounds for semilinear parabolic equations with nonlinear boundary conditions. Journal of Dynamics and Differential Equations, 16(1):91-138.
We consider a semilinear parabolic equation with a nonlinear non-dissipative boundary condition. In the one-dimensional case we describe bifurcation diagrams for positive and sign-changing equilibria and connecting orbits between these equilibria. We also show that the number of sign-changing stationary solutions strongly depends on the spatial dimension. The results are based on new a priori estimates of global solutions.
We consider a semilinear parabolic equation with a nonlinear non-dissipative boundary condition. In the one-dimensional case we describe bifurcation diagrams for positive and sign-changing equilibria and connecting orbits between these equilibria. We also show that the number of sign-changing stationary solutions strongly depends on the spatial dimension. The results are based on new a priori estimates of global solutions.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Uncontrolled Keywords: | emilinear parabolic equation - nonlinear boundary condition - blow-up - equilibrium - heteroclinic orbit - a priori estimates |
| Language: | English |
| Date: | 2004 |
| Deposited On: | 10 Jun 2010 12:56 |
| Last Modified: | 29 Jul 2020 19:39 |
| Publisher: | Springer |
| ISSN: | 1040-7294 |
| Additional Information: | The original publication is available at www.springerlink.com |
| OA Status: | Closed |
| Publisher DOI: | https://doi.org/10.1023/B:JODY.0000041282.14930.7a |
| Related URLs: | http://www.ams.org/mathscinet-getitem?mr=2093837 |
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Chipot, M