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On a fractional partial differential equation with dominating linear part
Author(s) -
Gripenberg G.,
Londen S.O.,
Prüss J.
Publication year - 1997
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19971110)20:16<1427::aid-mma937>3.0.co;2-y
Subject(s) - mathematics , monotone polygon , bounded function , sign (mathematics) , pure mathematics , partial differential equation , mathematical analysis , geometry
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 (−∞, 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 −α , b ( t )= t −β , and g (ξ)∼sign(ξ)∣ξ∣ γ for large ξ, then the main assumption is that α>(2γ+2)/(3γ+1)β+(2γ−2)/(3γ+1). © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.