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On an elasto-dynamic evolution equation with non dead load and friction. (English) Zbl 1164.34460
Summary: We are interested in the dynamic evolution of an elastic body, acted by resistance forces depending also on the displacements. We put the mechanical problem into an abstract functional framework, involving a second order nonlinear evolution equation with initial conditions. After specifying convenient hypotheses on the data, we prove an existence and uniqueness result. The proof is based on the Faedo-Galerkin method.
MSC:
34G20 Nonlinear differential equations in abstract spaces
34K07 Theoretical approximation of solutions to functional-differential equations
34K10 Boundary value problems for functional-differential equations
47H05 Monotone operators and generalizations
74B20 Nonlinear elasticity
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