Perturbed evolution problems with absolutely continuous variation in time and applications
| Autor: | Warda Belhoula, M. D. P. Monteiro Marques, Charles Castaing, Dalila Azzam-Laouir |
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| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Integrable system Applied Mathematics 010102 general mathematics Hilbert space Fixed-point theorem Monotonic function Absolute continuity Lipschitz continuity 01 natural sciences 010101 applied mathematics symbols.namesake Monotone polygon Modeling and Simulation symbols Geometry and Topology Uniqueness 0101 mathematics Mathematics |
| Zdroj: | Journal of Fixed Point Theory and Applications. 21 |
| ISSN: | 1661-7746 1661-7738 |
| DOI: | 10.1007/s11784-019-0666-2 |
| Popis: | This paper is devoted to the existence and uniqueness of absolutely continuous solutions in evolution problems of the form $$-\frac{\mathrm{{d}}u}{\mathrm{{d}}t}(t) \in A(t)u(t) + f(t, u(t))$$ in a new setting. For each t, $$A(t) : D(A(t)) \rightarrow 2 ^H$$ is a maximal monotone operator in a Hilbert space H and the perturbation f is separately integrable on [0, T] and separately Lipschitz on H. It is assumed that $$t \mapsto A(t)$$ has absolutely continuous variation, in the sense of Vladimirov’s pseudo-distance. Some extensions are also provided allowing new applications of our results to a larger number of problems modeled by maximal monotone operators. In particular, we solve evolution problems with multivalued upper semicontinuous perturbations, by using a fixed point theorem. |
| Databáze: | OpenAIRE |
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