Resolvent kernels that constitute an approximation of the identity and linear heat-transfer problems

  • L. R Berrone


Sufficient conditions are obtained for a Volterra integral equation whose kernel depends on an increasing parameter a to admit an approximation of the identity with respect to a in the form of a resolvent kernel. In this case, the solution of the integral equation tends to zero as a tends to infinity, and we establish estimates of this convergence in L. These results are used for obtaining estimates of the convergence of linear heat-transfer boundary conditions to Dirichlet ones as the heat-transfer coefficient tends to infinity.
How to Cite
Berrone, L. R. “Resolvent Kernels That Constitute an Approximation of the Identity and Linear Heat-Transfer Problems”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 52, no. 2, Feb. 2000, pp. 165-82,
Research articles