Abstract
We investigate a certain stochastic partial differential equation which is defined on the unit interval with periodic boundary condition and takes values in a manifold. Such equation has particularly two different applications. Namely, it determines the evolution law of an interacting constrained system of continuum distributed over the unit circle, while it defines a diffusive motion of loops on a manifold. We establish the existence and uniqueness results and then show the smoothness property of the solutions. Some examples are given in the final section.
| Original language | English |
|---|---|
| Pages (from-to) | 257-288 |
| Number of pages | 32 |
| Journal | Journal of Functional Analysis |
| Volume | 109 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1992 Nov 1 |
| Externally published | Yes |
Fingerprint
ASJC Scopus subject areas
- Analysis
Cite this
A stochastic partial differential equation with values in a manifold. / Funaki, Tadahisa.
In: Journal of Functional Analysis, Vol. 109, No. 2, 01.11.1992, p. 257-288.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A stochastic partial differential equation with values in a manifold
AU - Funaki, Tadahisa
PY - 1992/11/1
Y1 - 1992/11/1
N2 - We investigate a certain stochastic partial differential equation which is defined on the unit interval with periodic boundary condition and takes values in a manifold. Such equation has particularly two different applications. Namely, it determines the evolution law of an interacting constrained system of continuum distributed over the unit circle, while it defines a diffusive motion of loops on a manifold. We establish the existence and uniqueness results and then show the smoothness property of the solutions. Some examples are given in the final section.
AB - We investigate a certain stochastic partial differential equation which is defined on the unit interval with periodic boundary condition and takes values in a manifold. Such equation has particularly two different applications. Namely, it determines the evolution law of an interacting constrained system of continuum distributed over the unit circle, while it defines a diffusive motion of loops on a manifold. We establish the existence and uniqueness results and then show the smoothness property of the solutions. Some examples are given in the final section.
UR - http://www.scopus.com/inward/record.url?scp=38249009358&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=38249009358&partnerID=8YFLogxK
U2 - 10.1016/0022-1236(92)90019-F
DO - 10.1016/0022-1236(92)90019-F
M3 - Article
AN - SCOPUS:38249009358
VL - 109
SP - 257
EP - 288
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 2
ER -