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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Global smooth solutions for a class of
parabolic integrodifferential equations

Author: Hans Engler
Journal: Trans. Amer. Math. Soc. 348 (1996), 267-290
MSC (1991): Primary 45K05
MathSciNet review: 1321573
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Abstract: The existence and uniqueness of smooth global large data solutions of a class of quasilinear partial integrodifferential equations in one space and one time dimension are proved, if the integral kernel behaves like $t^{-\alpha }$ near $t=0$ with $\alpha > 2/3$. An existence and regularity theorem for linear equations with variable coefficients that are related to this type is also proved in arbitrary space dimensions and with no restrictions for $\alpha $.

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Additional Information

Hans Engler

Keywords: Integrodifferential equation, quasilinear, regular solution, global existence, regularity, singular kernel
Received by editor(s): September 22, 1994
Received by editor(s) in revised form: January 13, 1995
Additional Notes: Supported by the National Science Foundation under grant # DMS-9003543
Article copyright: © Copyright 1996 American Mathematical Society