Analysis of the nonlocal wave propagation problem with volume constraints

: pp. 334–344
Received: June 12, 2020
Revised: July 24, 2020
Accepted: July 27, 2020
Cadi Ayyad University
Institut Polytechnique UniLaSalle
Cadi Ayyad University
Sultan Moulay Slimane University

In the current paper, we develop a nonlocal propagation model, which describes the diffusion wave process.  The main motivation of this work is to apply the nonlocal vector calculus, introduced and developed by Du et al. [1] to such hyperbolic problem.  Moreover, based on some density arguments, some a priori estimates and using the Galerkin approach, we prove existence and uniqueness of a weak solution to the nonlocal wave equation widely adopted in various applications.

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Mathematical Modeling and Computing, Vol. 7, No. 2, pp. 334–344 (2020)