Global smooth solutions for a class of parabolic integrodifferential equations

Engler, Hans

doi:10.1090/S0002-9947-96-01472-9

Global smooth solutions for a class of parabolic integrodifferential equations
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by Hans Engler

Trans. Amer. Math. Soc. 348 (1996), 267-290

DOI: https://doi.org/10.1090/S0002-9947-96-01472-9

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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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