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Parabolic Problems and Boundary Integral Equations
Author(s) -
Baderko Elena A.
Publication year - 1997
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19970325)20:5<449::aid-mma818>3.0.co;2-e
Subject(s) - mathematics , mathematical analysis , integral equation , singular integral , boundary value problem , parabolic partial differential equation , bounded function , corollary , volterra integral equation , partial differential equation , pure mathematics
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 Hölder 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 Hölder spaces for initial boundary value parabolic problems. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.