WEAK SOLUTIONS OF HYPERBOLIC-PARABOLIC VOLTERRA-EQUATIONS

Authors
Citation
G. Gripenberg, WEAK SOLUTIONS OF HYPERBOLIC-PARABOLIC VOLTERRA-EQUATIONS, Transactions of the American Mathematical Society, 343(2), 1994, pp. 675-694
Citations number
32
Categorie Soggetti
Mathematics, General",Mathematics
ISSN journal
00029947
Volume
343
Issue
2
Year of publication
1994
Pages
675 - 694
Database
ISI
SICI code
0002-9947(1994)343:2<675:WSOHV>2.0.ZU;2-J
Abstract
The existence of a global weak solution, satisfying certain a priori L (infinity)-bounds, of the equation u(t)(t,x) = integral-t/0 k(t-s)(sig ma(u(x)))x(s,x)ds + f(t,x) is established. The kernel k is locally int egrable and log-convex, and sigma' has only one local minimum which is positive.