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arXiv · 1509.03133

Transmission problems with nonlocal boundary conditions and rough dynamic interfaces

Ciprian G. Gal·Mahamadi Warma
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Abstract

We consider a transmission problem consisting of a semilinear parabolic equation in a general non-smooth setting with emphasis on rough interfaces which bear a fractal-like geometry and nonlinear dynamic (possibly, nonlocal)\ boundary conditions along the interface. We give a unified framework for existence of strong solutions, existence of finite dimensional attractors and blow-up phenomena for solutions under general conditions on the bulk and interfacial nonlinearities with competing behavior at infinity.

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Ciprian G. Gal, Mahamadi Warma. 2015-09-10. Transmission problems with nonlocal boundary conditions and rough dynamic interfaces. https://doi.org/10.1088/0951-7715%2F29%2F1%2F161

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