TY - JOUR
T1 - A stochastic partial differential equation with values in a manifold
AU - Funaki, Tadahisa
N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
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.
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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 -