Semilinear evolution transmission problems across fractal layers |
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| Authors: | Maria Rosaria Lancia Paola Vernole |
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| Affiliation: | 1. Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza Università di Roma, Via A. Scarpa 16, 00161 Roma, Italy;2. Dipartimento di Matematica, Sapienza Università di Roma, P.zale Aldo Moro 2, 00185 Roma, Italy |
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| Abstract: | A semilinear parabolic transmission problem across either a fractal layer S or the corresponding prefractal layer Sh is studied. Local existence, uniqueness and regularity results for the mild solution, in both cases, are established as well as a sufficient condition on the initial datum for global existence is given. The asymptotic behaviour of the solutions of the approximating problems is studied. |
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| Keywords: | 31C25 35K55 47D06 28A80 |
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