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Equilibria, Connecting Orbits and a Priori Bounds for Semilinear Parabolic Equations with Nonlinear Boundary Conditions |
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| Authors: | Michel Chipot Pavol Quittner |
| Affiliation: | (1) Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057, Zürich, Switzerland. E-mail:;(2) Institute of Applied Mathematics, Comenius University, Mlynská dolina, SK-84248, Bratislava, Slovakia. E-mail: |
| Abstract: | 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. |
| Keywords: | Semilinear parabolic equation nonlinear boundary condition blow-up equilibrium heteroclinic orbit a priori estimates |
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