Theoretical and Numerical Studies of High-Order Problems

Abstract

In this thesis, we aim to conduct analytical and approximate (numerical) studies on higher-order partial differential equations. In the first work, we investigate a class of nonlinear parabolic integro-differential equations with an unknown flux on a part of the Dirichlet boundary, treating it both analytically and numerically. To this end, we employ the Rothe method. The second work is primarily theoretical, we study hyperbolic p(.)-biharmonic equation with no flux boundary condition. We prove the existence and blow-up behavior of the weak solution using the Galerkin method. Finally, in the third work, we show the approximation studies to evolution p-biharmonic problem employing the mixed finite element method combined with the Rothe method.