Perron's method for second order hyperbolic PDE. Part I |
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Authors: | Penny Smith |
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Affiliation: | Department of Mathematics, Lehigh University, 27 Memorial Drive West, Bethlehem, PA 18015, USA |
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Abstract: | In parts I, II, and III combined of this paper, we define a notion of viscosity solution for these equations and existence is proved by a Perron-like method. Here, in part I, we prove useful identities, and a maximum-like principle for smooth sub(super) solutions of the standard wave equation. We define a new potential theoretic (P) notion of solution, subsolution and supersolution, and a related potential type (P) Cauchy problem for semilinear second order hyperbolic equations. |
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