Analysis of a scalar nonlocal peridynamic model with a sign changing kernel

Tadele Mengesha; Qiang Du

doi:10.3934/dcdsb.2013.18.1415

Article Contents

2013, Volume 18, Issue 5: 1415-1437. Doi: 10.3934/dcdsb.2013.18.1415

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Analysis of a scalar nonlocal peridynamic model with a sign changing kernel

Tadele Mengesha^1, and
Qiang Du^1,

1.
Department of Mathematics, Pennsylvania State University, University Park, PA 16802

Received: December 31, 2012

Revised: January 31, 2013

Published: June 2013

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Abstract

In this paper, a scalar peridynamic model is analyzed. The study extends earlier works in the literature on scalar nonlocal diffusion and nonlocal peridynamic models to include a sign changing kernel. We prove the well-posedness of both variational problems with nonlocal constraints and time-dependent equations with or without damping. The analysis is based on some nonlocal Poincaré type inequalities and compactness of the associated nonlocal operators. It also offers careful characterizations of the associated solution spaces such as compact embedding, separability and completeness along with regularity properties of solutions for different types of kernels.

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Mathematics Subject Classification: 45A05, 45K05, 47G10, 74G65, 74H20, 74H25.

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