Piecewise Continuous Solutions of Pseudoparabolic Equations in Two Space Dimensions.
DELAWARE UNIV NEWARK INST FOR MATHEMATICAL SCIENCES
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One of the principal boundary value problems in analytic function theory is the so-called Riemann boundary value problem. The simplest version of the problem requires the finding of an analytic function phi in CGamma, where Gamma is a closed smooth contour, and a prescribed Hoelder continuous jump is prescribed for phi across Gamma. The solution of this problem may be given in terms of a Cauchy integral. In generalized analytic, as well as generalized hyperanalytic function theory, a Cauchy-type representation exists, which suggest that the Riemann problem may be solved in a similar way. In the present work several new representations for initial value problems are obtained. An iterative scheme is presented for solving the initial-boundary value problem. These results are of interest for investigating wave motion in anisotropic, nonhomogeneous elastic materials.
- Numerical Mathematics