Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 348, Issue 1, Pages 137-149Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2008.06.054
Keywords
integro-differential equation; quasilinear equation; fractional derivative; completely positive kernel; weak solution; energy estimates; De Giorgi technique
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We investigate linear and quasilinear evolutionary partial integro-differential equations of second order which include time fractional evolution equations of time order less than one. By means of suitable energy estimates and De Giorgi's iteration technique we establish results asserting the global boundedness of appropriately defined weak solutions of these problems. We also show that a maximum principle holds for such equations. (C) 2008 Elsevier Inc. All rights reserved.
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