Mathematical behavior of partial differential equations with variable coefficients

In this thesis, we study the existence and uniqueness of the initial and boundary value problem for a class of higher order semilinear parabolic partial differential equations with constant and variable coefficient. Based on the priori estimates of the solution, the existence of the weak solution in the form of Fourier series under suitable conditions is proved. For this purpose Picard's successive approximation method is used. Also, the uniqueness of the weak solution is proved.