
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(ts). 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