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Zeitschrift für Analysis und ihre Anwendungen


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Volume 18, Issue 4, 1999, pp. 939–951
DOI: 10.4171/ZAA/922

Published online: 1999-12-31

Nonlinear Hyperbolic Equations with Dissipative Temporal and Spatial Non-Local Memory

F. Mošna[1] and Jindřich Nečas[2]

(1) Charles University, Prague, Czech Republic
(2) Charles University, Prague, Czech Republic

The equation governing the evolution of a displacement vector in an elastic body with dissipative temporal and spatial non-local memory is considered. The memory term is generated by a singular but integrable kernel. The existence of a global weak solution to the associated initial- boundary problem is established by constructing Calerkin approximations and deriving a suitable energy estimate.

Keywords: Singular viscoelasticity, energy estimates, weak solutions

Mošna F., Nečas Jindřich: Nonlinear Hyperbolic Equations with Dissipative Temporal and Spatial Non-Local Memory. Z. Anal. Anwend. 18 (1999), 939-951. doi: 10.4171/ZAA/922