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Convergence of solutions to the equation of quasi-static approximation of viscoelasticity with capillarity. (English) Zbl 0919.35022
The long time behavior of a solution to the equation \[ \text{div}(DW(\nabla u))+\Delta u_t- \delta^2\Delta^2 u= 0, \] augmented with initial and boundary conditions is investigated. A basic assumption is that the nonlinear term is real analytic. The main result asserts that all solutions converge to an equilibrium point, even if the initial conditions are quite rough. The result is valid without any assumption on the structure of the equilibria set.

MSC:
35B40 Asymptotic behavior of solutions to PDEs
74Hxx Dynamical problems in solid mechanics
35K35 Initial-boundary value problems for higher-order parabolic equations
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