The solvability of a strongly-coupled nonlocal system of equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:486

Article

关键词: Peridynamics;    Bessel potential space;    Nonlocal hyperbolic systems;    Nonlocal elliptic systems;    Fourier multipliers;    Semigroups;   

DOI  :  10.1016/j.jmaa.2020.123919

来源: Elsevier

【 摘 要 】

We prove existence and uniqueness of strong (pointwise) solutions to a linear nonlocal strongly coupled hyperbolic system of equations posed on all of Euclidean space. The system of equations comes from a linearization of a nonlocal model of elasticity in solid mechanics. It is a nonlocal analogue of the Navier-Lame system of classical elasticity. We use a well-known semigroup technique that hinges on the strong solvability of the corresponding steady-state elliptic system. The leading operator is an integro-differential operator characterized by a distinctive matrix kernel which is used to couple differences of components of a vector field. For an operator possessing an asymmetric kernel comparable to that of the fractional Laplacian, we prove the L-2-solvability of the elliptic system in a Bessel potential space using the Fourier transform and a priori estimates. This L-2-solvability together with the Hille-Yosida theorem is used to prove the well posedness of the wave-type time dependent problem. For the fractional Laplacian kernel we extend the solvability to L-p spaces using classical multiplier theorems. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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