Martingale Solutions Of Two Types Of Stochastic Nonlocal Partial Differential Equations On A Bounded Interval

Burgers equation and Ginzburg-Landau equation simulate propaga-tion of shockwave and superconductor respectively,which has aroused great attention of physicists and mathematicians.We are primarily interested in stochastic nonlocal generalized Burgers equation and Ginzburg-Landau equation on a bounded interval,and prove the existence of martingale solutions.In Chapter 1,we introduce physical background and known researching of Burg-ers equation and Ginzburg-Landau equation,state the definitions,inequalities and lem-mas which will be used in the paper,and give the main results of this thesis.In Chapter 2,we obtain stochastic nonlocal generalized Burgers equation on a bounded interval.Firstly,by considering stochastic nonlocal generalized Burgers e-quation in a fractional weighted Sobolev space,we overcome the difficulties of the nonlocal Laplacian operator on a bounded interval.Then,applying Galerkin approx-imation,Prokhorov theorem,Skorokhod theorem and martingale representation the-orem,it establishes the existence of martingale solutions for the stochastic nonlocal generalized Burgers equation on a bounded interval.In Chapter 3.According to the similar methods of Chapter 2,we obtain the ex-istence of martingale solutions for the stochastic nonlocal Ginzburg-Landau equation on a bounded interval.The final chapter states the outlook and thinking of the future research work.