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Global Smooth Solutions for a Class of Parabolic Integrodifferential Equations

Hans Engler
Transactions of the American Mathematical Society
Vol. 348, No. 1 (Jan., 1996), pp. 267-290
Stable URL: http://www.jstor.org/stable/2155176
Page Count: 24
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Global Smooth Solutions for a Class of Parabolic Integrodifferential Equations
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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-α 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 α.

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