Mathematical behavior of solutions of nonlinear parabolic partial differential equations

In this thesis, the mathematical behaviour of solutions of nonlinear parabolic partial differential equations is investigated.In the first chapter, so far the studies done with the historical developments are shortly given about parabolic partial differential equations.In the second chapter, some fundamental definitons and notations which are necessary for the remaining chapters of the thesis are presented.Weak solutions of the second order parabolic equations is presented in the third chapter.In the fourth chapter, local and global existence and asymptotic behaviour of Cauchy problem for a nonlinear pseudo-parabolic equation are investigated.In the fifth chapter, local and global existence, continuous dependence on initial data of a fourth order Cauchy problem with damping term is proved.