Existence and regularity results for terminal value problem for nonlinear fractional wave equations
We consider the terminal value problem (or called nal value problem, initial inverse prob- lem, backward in time problem) of determining the initial value, in a general class of time-fractional wave equations with Caputo derivative, from a given nal value. We are concerned with the existence, regula...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/116568 |
| Acceso en línea: | https://hdl.handle.net/11441/116568 https://doi.org/10.1088/1361-6544/abc4d9 |
| Access Level: | acceso abierto |
| Palabra clave: | Fractional derivatives and integrals Caputo fractional derivative terminal value problem time fractional wave equation wellposedness regularity estimates |
| Sumario: | We consider the terminal value problem (or called nal value problem, initial inverse prob- lem, backward in time problem) of determining the initial value, in a general class of time-fractional wave equations with Caputo derivative, from a given nal value. We are concerned with the existence, regularity of solutions upon the terminal value. Under several assumptions on the nonlinearity, we address and show the well-posedness (namely, the existence, uniqueness, and continuous dependence) for the terminal value problem. Some regularity results for the mild solution and its derivatives of rst and fractional orders are also derived. The e ectiveness of our methods are shown by applying the results to two interesting models: time fractional Ginzburg-Landau equation, and time fractional Burgers equation, where time and spatial regularity estimates are obtained. |
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