Zeitschrift für Analysis und ihre Anwendungen
Vol. 18, No. 4, pp. 939-951 (1999)
Nonlinear Hyperbolic Equations with Dissipative Temporal and Spatial Non-Local Memory
F. Mo\v sna and J. Ne\v casF. Mo\v sna: Charles Univ., Fac. Educ., M. D. Rettigové 4, 116 39 Praha 1, Czech Republic; J. Ne\v cas: Charles Univ., Fac. Math. & Phys., Sokolovská 83, 186 00 Praha 8, Czech Republic, and Nothern Illinois Univ., Dept. Math. Sci., DeKalb, Illinois 60115, USA
Abstract: 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 Galerkin approximations and deriving a suitable energy estimate.
Keywords: singular viscoelasticity, energy estimates, weak solutions
Classification (MSC2000): 45K05, 73F15
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