Computation Of Multiple Solutions To System Of P-lapiacian Equations

This paper is for designing a numerical method for calculating multiple solutions of systemof p-Laplacian equations. System of p-Laplacian equations has application in the study of non-Newtonian fluid, nonlinear elasticity and glaciology. On the other hand, it has been paid a lot ofattention in the study of differential equation theory. A few conclusions on existence of solutionshave been obtained. But, there is no effective method in the literature to numerically solve thesystem. Due to Banach space setting of the system and multiplicity of its solutions, it becomesdifficult to devise a numerical method. In this thesis, we shall take advantage of variational struc-ture of the system to design a min-orthogonal algorithm by pseudo-gradient and pseudo-gradientflow. Numerical experiment results presented in the thesis show that the algorithm is successful.Convergence results of the algorithm are also established. In addition, the descent efficiency ofmin-orthogonal algorithm is discussed and the way to raise the efficiency is suggested.