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Existence of solutions to nonlinear advection-diffusion equation applied to Burgers’ equation using Sinc methods. (English) Zbl 1340.35129
Summary: This paper has two objectives. First, we prove the existence of solutions to the general advection-diffusion equation subject to a reasonably smooth initial condition. We investigate the behavior of the solution of these problems for large values of time. Secondly, a numerical scheme using the Sinc-Galerkin method is developed to approximate the solution of a simple model of turbulence, which is a special case of the advection-diffusion equation, known as Burgers’ equation. The approximate solution is shown to converge to the exact solution at an exponential rate. A numerical example is given to illustrate the accuracy of the method.
35K57 Reaction-diffusion equations
35A01 Existence problems for PDEs: global existence, local existence, non-existence
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
Full Text: DOI
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