APPROXIMATION OF ABSTRACT QUASILINEAR EVOLUTION EQUATIONS IN THE SENSE OF HADAMARD

Abstract

An approximation theorem is given for abstract quasilinear evolution equations in the sense of Hadamard. A stability condition is proposed under which a sequence of approximate solutions converges to the solution. The result obtained in this paper is a generalization of an approximation theorem of regularized semigroups and is applied to an approximation problem for a degenerate Kirchhoff equation.