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arXiv · 1404.3429

Homotopy invariants methods in the global dynamics of strongly damped wave equation

Piotr Kokocki
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Abstract

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.

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Piotr Kokocki. 2014-04-13. Homotopy invariants methods in the global dynamics of strongly damped wave equation. https://arxiv.org/abs/1404.3429

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