Transmission problems with nonlocal boundary conditions and rough dynamic interfaces
arXiv:1509.03133 · doi:10.1088/0951-7715/29/1/161
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.
29 pages, 1 figure. arXiv admin note: text overlap with arXiv:1503.05744