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Elliptic and parabolic equations with fractional diffusion and dynamic boundary conditions

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  • We investigate a class of semilinear parabolic and elliptic problems with fractional dynamic boundary conditions. We introduce two new operators, the so-called fractional Wentzell Laplacian and the fractional Steklov operator, which become essential in our study of these nonlinear problems. Besides giving a complete characterization of well-posedness and regularity of bounded solutions, we also establish the existence of finite-dimensional global attractors and also derive basic conditions for blow-up.
    Mathematics Subject Classification: Primary: 35J92, 35A15, 35B41; Secondary: 35K65.


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