TY - GEN
T1 - Curvature motion perturbed by a direction-dependent colored noise
AU - Denis, Clément
AU - Funaki, Tadahisa
AU - Yokoyama, Satoshi
N1 - Publisher Copyright:
© Springer International Publishing AG, part of Springer Nature 2018.
PY - 2018
Y1 - 2018
N2 - The aim of this paper is twofold. First we give a brief overview of several results on the deterministic and stochastic motions by mean curvature and their derivation under the so-called sharp interface limit. Then, we study the motions by mean curvature perturbed by a direction-dependent Gaussian colored noise described by V=κ + W(t, n). This part is a generalization of (Funaki, Acta Math Sin (Engl Ser), 15:407–438, 1999) [10] where the noise is independent from space. We derive a uniform moment estimate on solutions of approximating equations and prove a Wong–Zakai type convergence theorem (in law) for the SPDEs for the curvature of a convex curve in two-dimensional space before the time the curve exhibits a singularity.
AB - The aim of this paper is twofold. First we give a brief overview of several results on the deterministic and stochastic motions by mean curvature and their derivation under the so-called sharp interface limit. Then, we study the motions by mean curvature perturbed by a direction-dependent Gaussian colored noise described by V=κ + W(t, n). This part is a generalization of (Funaki, Acta Math Sin (Engl Ser), 15:407–438, 1999) [10] where the noise is independent from space. We derive a uniform moment estimate on solutions of approximating equations and prove a Wong–Zakai type convergence theorem (in law) for the SPDEs for the curvature of a convex curve in two-dimensional space before the time the curve exhibits a singularity.
KW - Colored noise
KW - Motion by mean curvature
KW - Stochastic partial differential equation
KW - Wong–Zakai theorem
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U2 - 10.1007/978-3-319-74929-7_9
DO - 10.1007/978-3-319-74929-7_9
M3 - Conference contribution
AN - SCOPUS:85049969274
SN - 9783319749280
T3 - Springer Proceedings in Mathematics and Statistics
SP - 177
EP - 200
BT - Stochastic Partial Differential Equations and Related Fields - In Honor of Michael Röckner SPDERF, 2016
A2 - Trutnau, Gerald
A2 - Eberle, Andreas
A2 - Hoh, Walter
A2 - Kassmann, Moritz
A2 - Grothaus, Martin
A2 - Stannat, Wilhelm
PB - Springer New York LLC
T2 - International conference on Stochastic Partial Differential Equations and Related Fields, SPDERF 2016
Y2 - 10 October 2016 through 14 October 2016
ER -