Abstract
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.
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Berrone, L.R. Resolvent kernels that constitute an approximation of the identity and linear heat-transfer problems. Ukr Math J 52, 183–203 (2000). https://doi.org/10.1007/BF02529633
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DOI: https://doi.org/10.1007/BF02529633