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Parabolic Problems and Boundary Integral Equations

✍ Scribed by Elena A. Baderko

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
277 KB
Volume
20
Category
Article
ISSN
0170-4214

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✦ Synopsis

Communicated by W. Wendland

Dedicated to Professor George C. Hsiao on the occasion of his 60th birthday

Here we consider initial boundary value problems for parabolic equations in non-bounded (with respect to time) domains by using the single-layer potential. We discuss the solvability in anisotropic Ho¨lder spaces of the boundary integral equations, to which original parabolic problems are reduced. We construct the special operators (regularizers) for these integral equations which transform them to equivalent integral Volterra equations of the second kind with weakly singular kernels. As a corollary we obtain the theorem about the classical solvability in anisotropic Ho¨lder spaces for initial boundary value parabolic problems.

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