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On the relation of the operator ∂/∂s+∂/∂τ to evolution governed by accretive operators

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Abstract

Existence theorems for the equationdu/dt+Au=f(t), whereA is an accretive operator in a general Banach spaceX, are typically proved by showing that limits of solutions of discrete approximations to the equation exist. Here the estimates required to show this convergence are exhibited as special cases of estimates relating solutions of difference schemes for ∂/∂s+∂/∂τ to exact solutions.

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Authors and Affiliations

  1. Mathematics Research Center, University of Wisconsin, Madison, Wisconsin, U.S.A.

    Michael G. Crandall & L. C. Evans

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  1. Michael G. Crandall
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  2. L. C. Evans
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Sponsored by the United States Army under Contract No. DA-31-124-ARO-D-462.

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Crandall, M.G., Evans, L.C. On the relation of the operator ∂/∂s+∂/∂τ to evolution governed by accretive operators. Israel J. Math. 21, 261–278 (1975). https://doi.org/10.1007/BF02757989

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  • DOI: https://doi.org/10.1007/BF02757989

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