Approximation of solutions to evolution equations
Peter D. Miletta · Mathematical Methods in the Applied Sciences · 1994
Abstract The convergence of the Galerkin approximations to solutions of abstract evolution equations of the form u′(t)= − Au(t) + M(u(t)) is shown. Here A is a closed, positive definite, self‐adjoint linear operator with domain D(A) dense in a Hilbert space H and M is a non‐linear map defined on D(A½) which satisfies a Lipschitz condition on balls in D(A½).