The method of lines for the solutions of some nonlinear partial differential equations

AbstractIn this paper we deal with the method of lines in the case of certain first order nonlinear partial differential equations as well as equations of the parabolic type. A new aspect, compared to earlier investigations, is that the system we consider may contain partial and ordinary differential equations alike and, in addition the r.h.s. of the equations may involve some nonlinear operators. The domain of definition of the solutions is bounded by time dependent functions. Our general results are demonstrated on a simple system which describes a biological model