Article
ON INITIAL AND TERMINAL VALUE PROBLEMS FOR FRACTIONAL NONCLASSICAL DIFFUSION EQUATIONS
Author/s | NGuyen, Huy Tuan
Caraballo Garrido, Tomás |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2020-06-11 |
Deposit Date | 2021-02-01 |
Published in |
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Abstract | 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 ... 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. |
Funding agencies | Ministerio de Ciencia, Innovación y Universidades (MICINN). España Agencia Estatal de Investigación. España European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER) |
Project ID. | PGC2018-096540-B-I00 |
Citation | NGuyen, H.T. y Caraballo Garrido, T. (2020). ON INITIAL AND TERMINAL VALUE PROBLEMS FOR FRACTIONAL NONCLASSICAL DIFFUSION EQUATIONS. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 149 (1), 143-1-161-19. |
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