Boundary Layer Of Hsieh Equation With Conservative Nonlinearity

In this thesis,we consider an initial-boundary value problem of Hsieh equation with conservative nonlinearity.The global unique solvability in the framework of Sobolev is established.In particular,one of our main motivations is to investigate the boundary layer effect and the convergence rates as the diffusion parameter ?goes to zero.It is shown that the boundary layer thickness is of the order O(??)with 0<?<1/2.We need to point out that,different from the previous work on nonconservative form of Hsieh equations,the conservative nonlinearity(????)x implies that new nonlinear term ?x??? need to be handled.It is important that more regularities on the solution to the limit problem are required to obtain the convergence rates and boundary layer thickness.It is more difficult for initial-boundary problem due to lack of boundary conditions(especially,higher-order derivatives)prevents us from applying the integration by part to derive the energy estimates directly.Thus it is more complicated than the case of nonconservative form.Consequently more subtle mathematical analysis need to be introduced to overcome the difficulties.