ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

10. Partial Differential Equations

1991 MS Classification: 35, 60 Turo, Jan, Technical University of Gdansk, Poland Solution of first order stochastic functional partial differential equations via integral contractors M. Altman introduced the concept of contractors as a tool for solving deterministic equations in Banach spaces. In this paper we utilize the contractor theory to study the functional partial differential equations of first order with a random coefficient

\frac{∂u}{∂t}(t, x; ω) + \{a(t, x; ω) + b(t, x; ω)ẇ(t; ω)\}\frac{∂u}{∂x}(t, x; ω)
= f(t, x, u_{(t,x)}(ω); ω) + g(t, x, u_{(t,x)}(ω); ω)ẇ(t; ω), (t, x) ∈ I
u(t, x; ω) = φ(t, x; ω), (t, x) ∈ I_{0}, ω ∈ Ω,

where ẇ(t; ω) is the white noise process and u_{(t,x)} is the Hale-type operator. The formulation includes retarded argument and hereditary Volterra terms.