Existence and convergence results for infinite dimensional nonlinear stochastic equations with multiplicative noise
Tài liệu tham khảo
Attouch, 1984
H. Attouch, G. Buttazzo, G. Michaille, Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization, in: MPS/SIAM Series on Optimization, Philadelphia, PA, 2006.
Barbu, 2011, A variational approach to stochastic nonlinear parabolic problems, J. Math. Anal. Appl., 384, 2, 10.1016/j.jmaa.2010.07.016
Barbu, 2012, Optimal control approach to nonlinear diffusion equation driven by Wiener noise, J. Optim. Theory Appl., 153, 1, 10.1007/s10957-011-9946-8
Barbu, 2010
Barbu, 2009, A PDE variational approach to image denoising and restoration, Nonlinear Anal. RWA, 10, 1351, 10.1016/j.nonrwa.2008.01.017
Barbu, 2009, Stochastic nonlinear diffusion equations with singular diffusivity, SIAM J. Math. Anal., 41, 1106, 10.1137/080718966
Barbu, 2009, Existence of strong solutions for stochastic porous media equation under general monotonicity conditions, Ann. Probab., 37, 428, 10.1214/08-AOP408
Barbu, 2008, Existence and uniqueness of nonnegative solutions to the stochastic porous media equation, Indiana Univ. Math. J., 57, 187, 10.1512/iumj.2008.57.3241
Barbu, 2011
Barbu, 2011, On a random scaled porous media equation, J. Differential Equations, 251, 2494, 10.1016/j.jde.2011.07.012
Brezis, 1976, Un principe variationnel associé à certaines équations paraboliques, Le cas indépendant du temps, C. R. Acad. Sci. Paris Sér. A–B, 282, A971
Brezis, 1976, Un principe variationnel associé à certaines équations paraboliques, Le cas dépendant du temps, C. R. Acad. Sci. Paris Sér. A–B, 282, A1197
Brzeźniak, 1988, A convergence result for stochastic partial differential equations, Stochastics, 24, 423, 10.1080/17442508808833526
Brzeźniak, 2006, Asymptotic compactness and absorbing sets for 2D stochastic Navier–Stokes equations on some unbounded domains, Trans. Amer. Math. Soc., 358, 5587, 10.1090/S0002-9947-06-03923-7
Da Prato, 2004
Da Prato, 1996, Fully nonlinear stochastic partial differential equations, SIAM J. Math. Anal., 27, 40, 10.1137/S0036141093256769
Da Prato, 2008
Doss, 1977, Liens entre equations differentielles stochastiques et ordinaires, Ann. Inst. H. Poincaré, 13, 99
Duncan, 2005, Stochastic equations in Hilbert space with a multiplicative fractional Gaussian noise, Stochastic Process. Appl., 115, 1357, 10.1016/j.spa.2005.03.011
Flandoli, 2005, Stationary conjugation of flows for parabolic SPDEs with multiplicative noise and some applications, Stochastic Anal. Appl., 22, 1385
Răşcanu, 2008, The fitzpatrick function—a bridge between convex analysis and multivalued stochastic differential equations, J. Convex Anal., 18, 105
Sussmann, 1978, On the gap between deterministic and stochastic ordinary differential equations, Ann. Probab., 6, 19, 10.1214/aop/1176995608
Visintin, 2008, Extension of the Brezis–Ekeland–Nayroles principle to monotone operators, Sci. Appl. Adv. Math., 18, 633