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.
Cite this article
F. Mošna, Jindřich Nečas, Nonlinear Hyperbolic Equations with Dissipative Temporal and Spatial Non-Local Memory. Z. Anal. Anwend. 18 (1999), no. 4, pp. 939–951