2,362 research outputs found
Hadamard well-posedness for a hyperbolic equation of viscoelasticity with supercritical sources and damping
Presented here is a study of a viscoelastic wave equation with supercritical
source and damping terms. We employ the theory of monotone operators and
nonlinear semigroups, combined with energy methods to establish the existence
of a unique local weak solution. In addition, it is shown that the solution
depends continuously on the initial data and is global provided the damping
dominates the source in an appropriate sense.Comment: The 2nd version includes a new proof of the energy identit
Convergence of the Crank-Nicolson-Galerkin finite element method for a class of nonlocal parabolic systems with moving boundaries
The aim of this paper is to establish the convergence and error bounds to the
fully discrete solution for a class of nonlinear systems of reaction-diffusion
nonlocal type with moving boundaries, using a linearized
Crank-Nicolson-Galerkin finite element method with polynomial approximations of
any degree. A coordinate transformation which fixes the boundaries is used.
Some numerical tests to compare our Matlab code with some existing moving
finite elements methods are investigated
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