SOLVABILITY OF NONLOCAL SYSTEMS RELATED TO PERIDYNAMICS

Kaßmann M, Mengesha T, Scott J (2019)
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS 18(3): 1303-1332.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | Englisch
 
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Autor*in
Kaßmann, MoritzUniBi; Mengesha, Tadele; Scott, James
Abstract / Bemerkung
In this work, we study the Dirichlet problem associated with a strongly coupled system of nonlocal equations. The system of equations comes from a linearization of a model of peridynamics, a nonlocal model of elasticity. It is a nonlocal analogue of the Navier-Lame system of classical elasticity. 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. The paper's main contributions are proving well-posedness of the system of equations and demonstrating optimal local Sobolev regularity of solutions. We apply Hilbert space techniques for well-posedness. The result holds for systems associated with kernels that give rise to non-symmetric bilinear forms. The regularity result holds for systems with symmetric kernels that may be supported only on a cone. For some specific kernels associated energy spaces are shown to coincide with standard fractional Sobolev spaces.
Erscheinungsjahr
2019
Zeitschriftentitel
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
Band
18
Ausgabe
3
Seite(n)
1303-1332
ISSN
1534-0392
eISSN
1553-5258
Page URI
https://pub.uni-bielefeld.de/record/2933905

Zitieren

Kaßmann M, Mengesha T, Scott J. SOLVABILITY OF NONLOCAL SYSTEMS RELATED TO PERIDYNAMICS. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. 2019;18(3):1303-1332.
Kaßmann, M., Mengesha, T., & Scott, J. (2019). SOLVABILITY OF NONLOCAL SYSTEMS RELATED TO PERIDYNAMICS. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 18(3), 1303-1332. doi:10.3934/cpaa.2019063
Kaßmann, M., Mengesha, T., and Scott, J. (2019). SOLVABILITY OF NONLOCAL SYSTEMS RELATED TO PERIDYNAMICS. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS 18, 1303-1332.
Kaßmann, M., Mengesha, T., & Scott, J., 2019. SOLVABILITY OF NONLOCAL SYSTEMS RELATED TO PERIDYNAMICS. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 18(3), p 1303-1332.
M. Kaßmann, T. Mengesha, and J. Scott, “SOLVABILITY OF NONLOCAL SYSTEMS RELATED TO PERIDYNAMICS”, COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, vol. 18, 2019, pp. 1303-1332.
Kaßmann, M., Mengesha, T., Scott, J.: SOLVABILITY OF NONLOCAL SYSTEMS RELATED TO PERIDYNAMICS. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. 18, 1303-1332 (2019).
Kaßmann, Moritz, Mengesha, Tadele, and Scott, James. “SOLVABILITY OF NONLOCAL SYSTEMS RELATED TO PERIDYNAMICS”. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS 18.3 (2019): 1303-1332.

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