\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

A stochastic mass conserved reaction-diffusion equation with nonlinear diffusion

  • * Corresponding author: Danielle Hilhorst

    * Corresponding author: Danielle Hilhorst 

The first author is supported by a public grant as part of the Investissement d'avenir project, reference ANR-11-LABX-0056-LMH, LabEx LMH

Abstract Full Text(HTML) Related Papers Cited by
  • In this paper, we prove a well posedness result for an initial boundary value problem for a stochastic nonlocal reaction-diffusion equation with nonlinear diffusion together with a nul-flux 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.

    Mathematics Subject Classification: Primary: 60H15, 60H30, 35K55, 35K57.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
  •   D. C. Antonopoulou , P. W. Bates , D. Blömker  and  G. D. Karali , Motion of a droplet for the stochastic mass-conserving allen-cahn equation, SIAM Journal on Mathematical Analysis, 48 (2016) , 670-708.  doi: 10.1137/151005105.
      C. Bauzet , G. Vallet  and  P. Wittbold , The cauchy problem for conservation laws with a multiplicative stochastic perturbation, Journal of Hyperbolic Differential Equations, 9 (2012) , 661-709.  doi: 10.1142/S0219891612500221.
      C. Bennett and R. C Sharpley, Interpolation of Operators, volume 129. Academic press, 1988.
      S. Boussaïd , D. Hilhorst  and  T. N. Nguyen , Convergence to steady states for solutions of a reaction-diffusion equation, Evol. Equ. Control Theory, 4 (2015) , 39-59.  doi: 10.3934/eect.2015.4.39.
      W. Cheney, Analysis for Applied Mathematics, Springer, 2001. doi: 10.1007/978-1-4757-3559-8.
      G. Da Prato  and  A. Debussche , Stochastic cahn-hilliard equation, Nonlinear Analysis: Theory, Methods & Applications, 26 (1996) , 241-263.  doi: 10.1016/0362-546X(94)00277-O.
      G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Cambridge university press, 2014. doi: 10.1017/CBO9781107295513.
      T. Funaki and S. Yokoyama, Sharp interface limit for stochastically perturbed mass conserving allen-cahn equation, arXiv preprint, arXiv: 1610.01263, 2016.
      L. Gawarecki and V. Mandrekar, Stochastic Differential Equations in Infinite Dimensions, Springer, 2011. doi: 10.1007/978-3-642-16194-0.
      B. Gess , Strong solutions for stochastic partial differential equations of gradient type, Journal of Functional Analysis, 263 (2012) , 2355-2383.  doi: 10.1016/j.jfa.2012.07.001.
      I. Karatzas and S. Shreve, Brownian Motion and Stochastic Calculus, volume 113. Springer Science & Business Media, 2013. doi: 10.1007/978-3-642-31898-6.
      N. V. Krylov  and  B. L. Rozovskii , Stochastic evolution equations. stochastic differential equations: Theory and applications, Journal of Soviet Mathematics, 14 (1981) , 1233-1277. 
      H. H. Kuo, Introduction to Stochastic Integration, Springer Science & Business Media, 2006.
      M. Marion , Attractors for reaction-diffusion equations: Existence and estimate of their dimension, Applicable Analysis, 25 (1987) , 101-147.  doi: 10.1080/00036818708839678.
      C. Prévôt and M. Röckner, A Concise Course on Stochastic Partial Differential Equations, volume 1905. Springer, 2007.
      M. Reiß, Stochastic Differential Equations, Lecture Notes, Humboldt University Berlin, 2003.
      J. Rubinstein  and  P. Sternberg , Nonlocal reaction-diffusion equations and nucleation, IMA Journal of Applied Mathematics, 48 (1992) , 249-264.  doi: 10.1093/imamat/48.3.249.
      R. Temam, Navier-stokes Equations, volume 2. North-Holland Amsterdam, revised edition 1979.
  • 加载中
SHARE

Article Metrics

HTML views(848) PDF downloads(263) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return