On initial and terminal value problems for fractional nonclassical diffusion equations
In this paper, we consider fractional nonclassical diffusion equations under two forms: initial value problem and terminal value problem. For an initial value problem, we study local existence, uniqueness, and continuous dependence of the mild solution. We also present a result on unique continuatio...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2020 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/104392 |
| Acesso em linha: | https://hdl.handle.net/11441/104392 https://doi.org/10.1090/proc/15131 |
| Access Level: | acceso abierto |
| Palavra-chave: | Fractional nonclassical diffusion equation well-posedness ill-posedness regularity estimates regularization and error estimate |
| Resumo: | In this paper, we consider fractional nonclassical diffusion equations under two forms: initial value problem and terminal value problem. For an initial value problem, we study local existence, uniqueness, and continuous dependence of the mild solution. We also present a result on unique continuation and a blow-up alternative for mild solutions of fractional pseudo-parabolic equations. For the terminal value problem, we show the well-posedness of our problem in the case 0 < α ≤ 1 and show the ill-posedness in the sense of Hadamard in the case α > 1. Then, under the a priori assumption on the exact solution belonging to a Gevrey space, we propose the Fourier truncation method for stabilizing the ill-posed problem. A stability estimate of logarithmic-type in Lq norm is first established. |
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