A well-posedness result for a mass conserved Allen-Cahn equation with nonlinear diffusion

Kettani, Perla El; Hilhorst, Danielle; Lee, Kai

  • Proceedings of Equadiff 14, Publisher: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing(Bratislava), page 201-210

Abstract

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In this paper, we prove the existence and uniqueness of the solution of the initial boundary value problem for a stochastic mass conserved Allen-Cahn equation with nonlinear diffusion together with a homogeneous Neumann boundary condition in an open bounded domain of ℝ n with a smooth boundary. We suppose that the additive noise is induced by a Q-Brownian motion.

How to cite

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Kettani, Perla El, Hilhorst, Danielle, and Lee, Kai. "A well-posedness result for a mass conserved Allen-Cahn equation with nonlinear diffusion." Proceedings of Equadiff 14. Bratislava: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing, 2017. 201-210. <http://eudml.org/doc/294887>.

@inProceedings{Kettani2017,
abstract = {In this paper, we prove the existence and uniqueness of the solution of the initial boundary value problem for a stochastic mass conserved Allen-Cahn equation with nonlinear diffusion together with a homogeneous Neumann boundary condition in an open bounded domain of $\mathbb \{R\}^n$ with a smooth boundary. We suppose that the additive noise is induced by a Q-Brownian motion.},
author = {Kettani, Perla El, Hilhorst, Danielle, Lee, Kai},
booktitle = {Proceedings of Equadiff 14},
keywords = {Stochastic nonlocal reaction-diffusion equation, monotonicity method, conservation of mass},
location = {Bratislava},
pages = {201-210},
publisher = {Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing},
title = {A well-posedness result for a mass conserved Allen-Cahn equation with nonlinear diffusion},
url = {http://eudml.org/doc/294887},
year = {2017},
}

TY - CLSWK
AU - Kettani, Perla El
AU - Hilhorst, Danielle
AU - Lee, Kai
TI - A well-posedness result for a mass conserved Allen-Cahn equation with nonlinear diffusion
T2 - Proceedings of Equadiff 14
PY - 2017
CY - Bratislava
PB - Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing
SP - 201
EP - 210
AB - In this paper, we prove the existence and uniqueness of the solution of the initial boundary value problem for a stochastic mass conserved Allen-Cahn equation with nonlinear diffusion together with a homogeneous Neumann boundary condition in an open bounded domain of $\mathbb {R}^n$ with a smooth boundary. We suppose that the additive noise is induced by a Q-Brownian motion.
KW - Stochastic nonlocal reaction-diffusion equation, monotonicity method, conservation of mass
UR - http://eudml.org/doc/294887
ER -

References

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  1. Antonopoulou, D. C., HASH(0x2b12e48), Bates, P. W., Blömker, D., Karali, G. D., Motion of adroplet for the stochastic mass-conserving Allen-Cahn equation, , in SIAM J. Math. Anal. 48 (2016), pp. 670–708. MR3459976
  2. Bauzet, C., Vallet, G., Wittbold, P., The Cauchy problem for conservation laws with a multiplicative stochastic perturbation, , J. Hyperbolic Differ. Equ. 9,4 (2012), pp. 661-709. MR3021756
  3. Bennett, C., Sharpley, R., Interpolation of Operators, , Academic Press, Vol. 129 (1988). MR0928802
  4. Boussaı̈d, S., Hilhorst, D., Nguyen, T., Convergence to steady state for the solutions of a nonlocal reaction-diffusion equation, , Evol. Equ. Control Theory 4,1 (2015), pp. 39-59. MR3356465
  5. Prato, G. Da, J.Zabczyk,, Stochastic equations in infinite dimensions, , Second edition. Encyclopedia of Mathematics and its Applications, 152 (2014), Cambridge University Press, Cambridge. MR3236753
  6. Kettani, P. El, Hilhorst, D., K.Lee,, A stochastic mass conserved reaction-diffusion equation with nonlinear diffusion, , preprint. MR3917782
  7. Gess, B., Strong solutions for stochastic partial differential equations of gradient type, , J. of Functional Analysis, vol. 263, no. 8 (2012), pp. 2355-2383. MR2964686
  8. Krylov, N. V., Rozovskii, B. L., Stochastic evolution equations, , J. of Soviet Mathematics, vol. 14 (1981), pp. 1233-1277. MR0570795
  9. Marion, M., Attractors for reaction-diffusion equations: existence and estimate of their dimension, , Applicable Analysis: An International Journal, 25:1-2 (1987), pp. 101-147. MR0911962
  10. Rubinstein, J., Sternberg, P., Nonlocal reaction-diffusion equations and nucleation, , IMA J. of Applied Mathematics, 48 (1992), pp. 249-264. MR1167735
  11. HASH(0x2b33508), [unknown], [11] R.Temam, //Navier-stokes equations/, Amsterdam: North-Holland, Vol. 2, revised edition (1979). MR0603444

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