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Random nonlinear evolution inclusions in reflexive Banach spaces
| Content Provider | Semantic Scholar |
|---|---|
| Author | Avgerinos, Evgenios Papageorgiou, Nikolaos S. |
| Copyright Year | 1988 |
| Abstract | In this paper we present two existence results for a large class of random, nonlinear, multivalued evolution equations defined in a reflexive, separable Banach space and involving an m-dissipative operator. Applications to random multivalued parabolic p.d.e.'s are presented. Our work unifies and extends earlier results of Kampe de Feriet, Gopalsamy and Bharucha-Reid, Becus and Itoh. 1. Introduction. Many problems in physics, engineering, biology and social sciences lead to mathematical equations. In these equations, the coefficients and the other parameters have their origin in experimental data and represent some kind of average value. Therefore in many instances due to wide variations of the data or even due to our own ignorance, it is appropriate to abandon the deterministic model in favor of a stochastic one. This is very nicely exemplified in the books of Bharucha-Reid (4) and Soong (21). In this paper we present two existence results for a class of random nonlinear multivalued evolution equations defined in a reflexive, separable Banach space. This class of evolution equations models linear and several nonlinear partial differential equations of parabolic type. So our work unifies and extends earlier works on random parabolic partial differential equations. In particular, Kampe de Feriet (12, 13) was the first to study the random heat equation. The randomness entered in the problem through the initial value data. Later Gopalsamy and Bharucha-Reid (10) and Becus (2) introduced also randomness in the boundary value and source terms. Finally Itoh (11), allowed randomness to appear also in the operator, which instead of the Laplacian, was a general random, single valued, everywhere defined continuous, accretive operator. Our results cover all the above-mentioned works. Let (I2, E) be a measurable space and X a separable Banach space. Through- out this work we will be using the following notations: P^C)(X) = {A C X: nonempty, closed, (convex)} and Pkc(X) = {A C X: nonempty, compact, convex}. A multifunction F: fi —► Pf(X) is said to be measurable if for every x G X, |
| Starting Page | 293 |
| Ending Page | 299 |
| Page Count | 7 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0002-9939-1988-0958086-6 |
| Volume Number | 104 |
| Alternate Webpage(s) | http://www.ams.org/journals/proc/1988-104-01/S0002-9939-1988-0958086-6/S0002-9939-1988-0958086-6.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0002-9939-1988-0958086-6 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
