Dissertation (MSc Mathematics)Many of physical processes are nonlinear in nature. Such processes are often conveniently described by problems for nonlinear partial differential equations. This fact explains a strong research interest to this field in recent years. In the present research, we introduce different approaches of investigation of nonlinear problems for parabolic differential equations and systems of parabolic differential equations in case when the domain of the process is unbounded. Also in this work we study one initial boundary value problem for nonlinear parabolic equation with unbounded domain. We obtain a number of a priori estimates and apply the Galerkin approach to prove for existence and uniqueness of the solution to the problem.