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In this paper, we study the asymptotic behavior of the solution of a semilinear problem and of a Stokes problem, with periodic data, when the size of the domain increases. In particular, we prove exponential convergence to the solution of the corresponding problem with periodic boundary conditions.
We consider the linear Primitive Equations of the ocean in the three-dimensional space, with horizontal periodic and vertical Dirichlet boundary conditions. Thanks to Fourier transforms we are able to calculate explicitly the pressure term. We then state existence, unicity and regularity results...
We prove the existence of Gevrey type solutions for locally analytic, nonlinear difference equations possessing a formal solution that belongs to some (generalized) Gevrey class of divergent power series in z −1/p . We consider different types of domains: domains bounded by a curve with...
We establish some decay properties of the semigroup generated by a linear integro-differential equation in a Hilbert space, which is an abstract version of the equation u t (t)−βΔu(t)−∫ 0 ∞ k(s)Δu(t−s) ds=0 describing hereditary heat conduction.
The main result of this paper establishes optimal pointwise bounds for the polarization tensors that appear in representation formulae for the voltage perturbations caused by low volume fraction inhomogeneities. Furthermore it is demonstrated how these pointwise bounds may be used to derive a...
The goal of the paper is to derive Strichartz estimates for solutions to wave equations with time-dependent coefficients belonging to C r , 2≤r≤2n+1, and generating an anisotropic speed of propagation. A stabilization condition for the coefficients is introduced. This condition allows to show...
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