The SMGT equation from the boundary: regularity and stabilization

Abstract

We consider the third-order (in time) linear equation known as SMGT-equation, as defined on a multidimensional bounded domain. Part A gives optimal interior and boundary regularity results from (Formula presented.)–Dirichlet or Neumann boundary terms. Explicit representation formulas are given that can be taken to define the notion of solution in the canonical case (Formula presented.), while the same regularity results hold for (Formula presented.) Part B considers the SMGT equation under Neumann dissipative boundary conditions and critical parameter (Formula presented.) and (Formula presented.) a.e. in Ω. We provide two results: (i) uniform stabilization under minimal checkable geometric conditions, and (ii) strong stabilization in the absence of geometrical conditions.

Publication Title

Applicable Analysis

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