The index theory for multivalued dynamical systems with applications to reaction-diffusion equations with discontinuous nonlinearity. (English) Zbl 1541.35086
Summary: In this paper, we develop first a theory of existence of index pairs for multivalued semiflows. We apply this result to a reaction-diffusion equation having a discontinuous nonlinearity which gives rise to a differential inclusion governed by the Heaviside function. Second, we prove that, in a suitable regular phase space, the Conley index of the non-zero fixed points of this inclusion is a pointed sphere.
MSC:
| 35B41 | Attractors |
| 35K57 | Reaction-diffusion equations |
| 35R70 | PDEs with multivalued right-hand sides |
| 37B30 | Index theory for dynamical systems, Morse-Conley indices |
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