Elliptic regularization for the semi-linear telegraph system |
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Authors: | NC Apreutesei B Djafari Rouhani |
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Institution: | a Department of Mathematics, Technical University “Gh. Asachi” of Iasi, Bd. Carol I, 700506 Iasi, Romania b Department of Mathematical Sciences, University of Texas at El Paso, 500 W. University Ave., El Paso, TX 79968, USA |
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Abstract: | The solution of the semi-linear telegraph system is compared with the solution of an elliptic regularization, to which one associates two-point boundary conditions. An asymptotic approximation for the solution of the elliptic regularization is constructed. The method employed here is the boundary function method due to Vishik and Lyusternik. The problem is singularly perturbed of elliptic-hyperbolic type. To conduct this analysis, high regularity with respect to t for the solutions of both problems is required. Finally, the order of this approximation is found in different spaces of functions. |
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Keywords: | 35B25 35J65 35L45 35L50 41A60 |
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