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Nonlocal Problems for Parabolic Inclusions
| Content Provider | Semantic Scholar |
|---|---|
| Author | Brown, Abdelkader Boucherif |
| Copyright Year | 2008 |
| Abstract | Let be a an open bounded domain in R , N 2; with a smooth boundary @ ; and T > 0. De ne D = (0; T ) and = @ [0; T ]: In this paper we are concerned with the existence of solutions of the following parabolic inclusion ut + Lu 2 F (x; t; u), (x; t) 2 D; u(x; t) = 0; (x; t) 2 subjected to the nonlocal condition u(x; 0) = R T 0 g(x; t; u(x; t))dt for x 2 : We provide su¢ cient conditions on L; F; g that guarantee the existence of at least one solution. Our technique is based on the Greens function for linear parabolic partial di¤erential equations, xed point theorems for multivalued maps. Keywords. parabolic problems; integral representation of solutions; multivalued maps; nonlocal conditions; xed point theorems. AMS (MOS) Subject Classi cation: 35K20; 35K55; 35K60; 35C15; 35A05; 35B50; 35R05; 35R70 1 Introduction Let be a an open bounded domain in R , N 2; with a smooth boundary @ : We denote the norm (usually the Euclidean norm) of x 2 by kxk : Let T be a positive real number. De ne D = (0; T ) and = @ [0; T ]: Our objective is to investigate the existence of solutions of the following parabolic problem with a |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.dam.brown.edu/lcds/publications/documents/Boucherif_01.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Aharonov–Bohm effect Cations Frontotemporal dementia Inclusion Bodies LU decomposition Map Nonlocal Lagrangian Parabolic antenna Quantum nonlocality Solutions VHDL-AMS |
| Content Type | Text |
| Resource Type | Article |
