Existence and convergence of approximate solutions for nonlinear measure driven differential systems

We investigate the existence and convergence of approximate solutions for measure driven nonlinear differential systems defined on a separable Hilbert space. The system is restricted to finite-dimensional subspaces by using projection operators. We utilize analytic semigroup theory to construct the space in which existence and convergence are studied. In particular, the approximate solutions in finite dimensions are considered, and their convergence is verified. We apply our major findings to a partial differential equation.