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dc.contributor.authorGal, Ciprian G.|Warma, Mahamadi|
dc.identifier.citationGal, C.G. & Warma, M. Z. (2016) Long-term behavior of reaction-diffusion equations with nonlocal boundary conditions on rough domains. Zeitschrift fur angewandte Mathematik und Physik 67: 83.
dc.identifier.issn0044-2275 |1420-9039|
dc.descriptionAuthor pre-print version. The publisher assign an article number, without range of pages. This article has 39 pages.
dc.description.abstractWe investigate the long term behavior in terms of finite dimensional global and exponential attractors, as time goes to infinity, of solutions to a semilinear reaction-diffusion equation on non-smooth domains subject to nonlocal Robin boundary conditions, characterized by the presence of fractional diffusion on the boundary. Our results are of general character and apply to a large class of irregular domains, including domains whose boundary is H?older continuous and domains which have fractal-like geometry. In addition to recovering most of the existing results on existence, regularity, uniqueness, stability, attractor existence, and dimension, for the well-known reaction-diffusion equation in smooth domains, the framework we develop also makes possible a number of new results for all diffusion models in other non-smooth settings.en_US
dc.description.sponsorshipThe work of the second author is partially supported by the Air Force Office of Scientific Research under the Award No: FA9550-15-1-0027.
dc.publisherSpringer International Publishing
dc.subjectThe Laplace operator |nonlocal Robin boundary conditions on non-smooth domains|global attractor|exponential attractor|fractal-like domains| domains with H?older cusps| semilinear reaction-diffusion equation|en_US
dc.titleLong-term behavior of reaction-diffusion equations with nonlocal boundary conditions on rough domainsen_US

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