GLOBAL SMOOTH SOLUTIONS FOR A CLASS OF PARABOLIC INTEGRODIFFERENTIAL EQUATIONS

Authors
ENGLER H
Citation
H. Engler, GLOBAL SMOOTH SOLUTIONS FOR A CLASS OF PARABOLIC INTEGRODIFFERENTIAL EQUATIONS, Transactions of the American Mathematical Society, 348(1), 1996, pp. 267-290
Citations number
33
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Transactions of the American Mathematical Society → ACNP
ISSN journal
00029947
Volume
348
Issue
1
Year of publication
1996
Pages
267 - 290
Database
ISI
SICI code
0002-9947(1996)348:1<267:GSSFAC>2.0.ZU;2-M
Abstract
The existence and uniqueness of smooth global large data solutions of a class of quasilinear partial integrodifferential equations in one sp ace and one time dimension are proved, if the integral kernel behaves like t(-alpha) near t = 0 with alpha > 2/3. An existence and regularit y theorem for linear equations with variable coefficients that are rel ated to this type is also proved in arbitrary space dimensions and wit h no restrictions for alpha.