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A class of nonlinear two-point boundary value problems with singular perturbations are studied. We show asymptotic behavior of the solutions of the perturbed systems and derive asymptotic expansions for the solutions of the perturbed systems, which can approximate the solutions of the perturbed...
For rapidly spatially oscillating nonlinearities f and inhomogeneities g we compare solutions u ε of reaction–diffusion systems ∂tu ε = aΔu ε − f(ε, x, x/ε, u) + g(ε, x, x/ε) with solutions u 0 of the formally homogenized, spatially averaged system ∂tu 0 = aΔu 0 − f 0 (x, u 0 )...
We study the approximation of a parabolic equation with a nonsmooth Dirichlet boundary condition by equations with Robin boundary conditions. We give the convergence rate, in some suitable anisotropic Sobolev spaces, of the penalized solution towards the Dirichlet solution when the penalty...
We consider the flow of two Newtonian, incompressible and nonmiscible fluids in a 2D thin domain. Starting from the Stokes equations, we derive a generalized Buckley-Leverett equation for the first fluid saturation. We study the asymptotic behavior of the flow when the thickness of the gap tends...
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