Numerical Solution of Problems which are not Well Posed in the Sense of Hadamardd

Abstract

Problems in partial differential equations usually require that a solution u of the differential equation is to be determined from certain data f. In a well posed problem in the sense of Hadamard u exists for all f of a certain class C s is uniquely determined by f and depends continuously on f. Well posed problems of this type are presented by the classical initial and boundary value problems of mathematical physics Existence of solutions has been established for rather general classes of such problems Considerable progress has also been made in constructing numerical schemes to approximate solutions: these schemes have to be stable in the sense that they furnish approximations which are represented by operators acting on the data f which are bounded uniformly