Probability methods and nonlinear analysis |
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Authors: | DJ Hebert |
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Institution: | Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260 USA |
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Abstract: | The concepts of accretive and differentiable operator in a Banach space B are used to show that certain approximations to a solution of a nonlinear evolution equation converge. When B is a space of continuous functions it is shown that the approximations and the solution be represented as integrals with respect to a signed measure on a function space. As an example, a new proof is given for the existence and uniqueness of solutions to a nonlinear parabolic differential equations with coefficients dependent upon solutions. Integral representations of these solutions follow. |
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