ON A FRACTIONAL PARTIAL-DIFFERENTIAL EQUATION WITH DOMINATING LINEAR PART

Authors
GRIPENBERG G LONDEN SO PRUSS J
Citation
G. Gripenberg et al., ON A FRACTIONAL PARTIAL-DIFFERENTIAL EQUATION WITH DOMINATING LINEAR PART, Mathematical methods in the applied sciences, 20(16), 1997, pp. 1427-1448
Citations number
10
Categorie Soggetti
Mathematical Method, Physical Science",Mathematics
Journal title
Mathematical methods in the applied sciences → ACNP
ISSN journal
01704214
Volume
20
Issue
16
Year of publication
1997
Pages
1427 - 1448
Database
ISI
SICI code
0170-4214(1997)20:16<1427:OAFPEW>2.0.ZU;2-8
Abstract
It is proved that there is a (weak) solution of the equation u(t) = a u(xx) + b * g(u(x))(x) + f, on R+ (where * denotes convolution over (-infinity, t)) such that u(x) is locally bounded. Emphasis is put on having the assumptions on the initial conditions as weak as possible. The kernels a and b are completely monotone and if a(t) = t(-alpha), b (t) = (t-beta), and g(xi) similar to sign(xi)/xi/(y) for large xi, the n the main assumption is that alpha > (2y + 2)/(3y + 1)beta + (2y - 2) /(3y + 1). (C) 1997 by B.G. Teubner Stuttgart-John Wiley & Sons Ltd.