Initial Problem Of Advectton Diffusion Equation With Disconuous Coefficients And Relevant Domain Decomposition Algorithm

Initial value problem of advection diffusion equations is a most popular topic inrecent years.There have been good results on continuous coefficient advectiondiffusion equations, and they are helpful to study of cases with variable coefficientand discontinuous coefficients.In thesis,we study the one-dimensional advectiondiffusion,we get solution in the L1space Referance Cauchy Problems and study itsconvergent.By the Schwarz waveform Relaxation method on continuous level,westudy the well–posedness and convergent of the solution on overlap domain ,andapply it to the nonoverlap case,then apply it to the discontinous case.This thesisinvestgates on well-posedness of convection diffusion equations with discontinouscoefficients and numerical algorithms of domain decomposition.In this thesis, westudy initial value problem of advection diffusion equation with discontinuouscoefficients and its domain decomposition algorithm.The first chapter introduces the convection diffusion equation and its applicationbackground, presents the problems to be studied in this thesis, and outlines theapparoaches to solve the problems.The second chapter studies the solution of the Cauchy problem ofone-dimensional advection diffusion equation with discontinous coefficients.Wedivide the problem into two problems: a degenerate problem and a regular problem,and show that these problems have unique solutions. We then derive and analyze theconvergence of sequence solutions of the regularized problem and the degengerateproblem as well.The third chapter investigates the classic Schwarz domain decomposition method,and focuses on the optimal Schwarz waveform relaxation algorithm. We analyze theRobin-type method of this problem, and show that the algorithm is well posseness andconvergence. Following this, we consider the application of the algorithm to annon-overlapping domain problem, and analyze its convergence and frequencyapproximation.In chapter four, we study the optimal Schwarz waveform relaxtion algorithm andRobin optimal Schwarz waveform relaxtion algorithm of advection diffusion equationwith discontinous coefficients,and analysis their well poseness and convergence.Atlast,we use the finite volume algorithm test the result and evolution of the solution.