Accession Number : AD0708143

Title :   SMOOTHNESS OF SOLUTIONS OF VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY SINGULAR KERNELS,

Corporate Author : BROWN UNIV PROVIDENCE R I

Personal Author(s) : Miller,Richard K. ; Feldstein,Alan

Report Date : JUN 1970

Pagination or Media Count : 35

Abstract : The purpose of the paper is to obtain results on the differentiability properties of solutions of nonlinear Volterra integral equations of the second kind with convolution kernels a(t-s). It is assumed that a(t) is continuous for t > 0 and integrable at the origin although a(t) may become unbounded at t = 0. Solutions are known to be continuous for all t = or > 0. The results in this paper prove that the solution x(t) is smooth for t > 0. The existence and the possible nature of singularities in x'(t) at t = 0 are studied for a large class of kernels. The special case a(t) = t to the power (-p) (0 < p < 1) is studied in particular detail. (Author)

Descriptors :   (*INTEGRAL EQUATIONS, THEOREMS), NUMERICAL INTEGRATION, NONLINEAR DIFFERENTIAL EQUATIONS, BOUNDARY VALUE PROBLEMS, NUMERICAL ANALYSIS, ERRORS

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE