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The Role of Surface Diffusion in Dynamic Boundary Conditions: Where Do We Stand?

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Abstract

In this study, we investigate reaction-diffusion and elliptic-like equations with two classes of dynamic boundary conditions, of reactive and reactive-diffusive type. We provide sharp upper and lower bounds on the dimension of the global attractor in all these cases. In particular, we emphasize how surface diffusion can act as a damping force in reducing the degree of complexity in these systems. We obtain a new Weyl asymptotic law for eigenvalue sequences associated with a family of perturbed Wentzell operators which is of independent interest.

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  1. Department of Mathematics, Florida International University, DM 435B, Miami, FL, 33199, USA

    Ciprian G. Gal

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Gal, C.G. The Role of Surface Diffusion in Dynamic Boundary Conditions: Where Do We Stand?. Milan J. Math. 83, 237–278 (2015). https://doi.org/10.1007/s00032-015-0242-1

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