Homotopy invariants methods in the global dynamics of strongly damped wave equation
| Autor: | Kokocki, Piotr |
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| Rok vydání: | 2014 |
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| Druh dokumentu: | Working Paper |
| Popis: | We are interested in the following differential equation $\ddot u(t) = -A u(t) - c A \dot u(t) + \lambda u(t) + F(u(t))$ where $c > 0$ is a damping factor, $A$ is a sectorial operator and $F$ is a continuous map. We consider the situation where the equation is at resonance at infinity, which means that $\lambda$ is an eigenvalue of $A$ and $F$ is a bounded map. We provide geometrical conditions for the nonlinearity $F$ and determine the Conley index of the set $K_\infty$, that is the union of the bounded orbits of this equation. Comment: 23 pages. arXiv admin note: substantial text overlap with arXiv:1310.6794 |
| Databáze: | arXiv |
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