Composite wave models for elastic plates

The long-term challenge of formulating an asymptotically motivated wave theory for elastic plates is addressed. Composite two-dimensional models merging the leading or higher-order parabolic equations for plate bending and the hyperbolic equation for the Rayleigh surface wave are constructed. Analysis of numerical examples shows that the proposed approach is robust not only at low- and high-frequency limits but also over the intermediate frequency range.

Higher-Order Parabolic Equations with VMO Assumptions and General Boundary Conditions with Variable Leading Coefficients

We prove weighted mixed $L_{p}(L_{q})$-estimates, with $p,q\in (1,\infty )$, and the corresponding solvability results for higher-order elliptic and parabolic equations on the half space ${\mathbb{R}}^{d+1}_{+}$ and on general $C^{2m-1,1}$ domains with general boundary conditions, which satisfy the Lopatinskii–Shapiro condition. We assume that the elliptic operators A have leading coefficients that are in the class of vanishing mean oscillations both in the time and the space variables and that the boundary operators have variable leading coefficients. The proofs are based on and generalize the estimates recently obtained by the authors in [6].