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Title: Boundary Wave and Interior Wave Propagations
Keywords: master relationship, Green's function, characteristic boundary,strong shock,wave interaction,nonlinear stability
Issue Date: 19-Aug-2013
Citation: DU LINGLONG (2013-08-19). Boundary Wave and Interior Wave Propagations. ScholarBank@NUS Repository.
Abstract: This thesis is concerned with the mathematical study of the boundary wave and interior wave propagation. The models we considered are the Broadwell model of the Boltzmann equation in the kinetic theory and a simplified model from magnetohydrodynamics (MHD). In the first part, the initial boundary value problem for the Broadwell model in the half space is studied to understand the interaction of boundary waves and interior fluid waves. The Green's function for the linearized system in the half space is constructed. Moreover, the optimal rate of convergence of the solution to a global Maxwellian is obtained by combining this Green's function for the half space with nonlinear terms. In the second part we study the interaction of interior nonlinear waves. We consider two models, one is a conservative system from the MHD, the other is the Broadwell model from the kinetic theory. We seek a unified approach to solve the linearized problem around the general shock profile with general amplitude, which is a variable coefficient PDE(system). With the explicit structure of solution for the linearized problem, we study the nonlinear wave propagation and to conclude the convergence with an optimal convergent rate around the shock front.
Appears in Collections:Ph.D Theses (Open)

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