Global Solution for a Stochastic Ginzburg-Landau Equation with Multiplicative Noise

References

• Bang , O. , Christiansen , P.L. , If , F. and Rasmussen , K.O. 1994 . Temperature effects in a nonlinear model of monolayer Scheibe aggregates . Phys. Rev. E. , 49 : 4627 – 4636 .
   PubMed Web of Science ®Google Scholar
• Bang , O. , Christiansen , P.L. , If , F. and Rasmussen , K.O. 1995 . White noise in the two-dimensional nonlinear Schrödinger equation . Appl. Anal. , 57 : 3 – 15 .
   Google Scholar
• Barton-Smith , M. 2003 . Invariant measure for stochastic Ginzburg–Landau equation . NoDEA , 10 : 95 – 117 .
   Web of Science ®Google Scholar
• Bechouche , J.P. and Jüngel , A. 2000 . Inviscid limits of the complex Ginzburg–Landau equation . Comm. Math. Phys. , 214 : 201 – 226 . [CROSSREF]
   Web of Science ®Google Scholar
• Brzezniak , Z. 1997 . On stochastic convolution in Banach spaces and applications . Stochastic Stochastic Reports , 61 : 245 – 295 .
   Google Scholar
• Brzezniak , Z. and Peszat , S. 1999 . Space-time continuous solutions to SPDE's driven by homogeneous Weiner process . Studia Mathematica , 137 ( 3 ) : 261 – 299 .
   Web of Science ®Google Scholar
• Cardon-Weber , C. 2001 . Cahn-Hilliard stochastic equation existence of the solution and of its density . Bernouilli , 7 ( 5 ) : 777 – 816 .
   Web of Science ®Google Scholar
• Cazenave, T. An Introduction to Nonlinear Schrödinger Equations; Textos de metodos matematicas, 26 Instituto de Matematica – UFRJ – (1996)
   Google Scholar
• Da Prato , G. and Gatarek , D. 1995 . Stochastic Burgers equation with correlated noise . Stochastics Stochastics Reports , 52 ( 1–2 ) : 29 – 41 .
   Google Scholar
• Da Prato, G.; Zabczyk, J. Stochastic equations in infinite dimensions. Encyclopedia of Mathematics
   Google Scholar
• de Bouard , A. and Debussche , A. 1999 . A stochastic nonlinear Schrödinger equation with multiplicative noise . Comm. Math. Phys. , 205 : 161 – 181 . [CROSSREF]
   Web of Science ®Google Scholar
• Debussche , A. and Di Menza , L. 2002 . Numerical simulation of focusing stochastic nonlinear Schrödinger equations . Physica D , 162 ( 3–4 ) : 131 – 154 .
   Web of Science ®Google Scholar
• Doering , C.R. , Gibbon , J.D. and Levermore , C.D. 1994 . Weak and strong solutions for the complex Ginzburg–Landau equation . Physica D , : 285 – 318 .
   Web of Science ®Google Scholar
• Golman , M. 1984 . Plasma turbulence . Rev. Mod. Phys. , 56 : 709 – 735 . [CROSSREF]
   Web of Science ®Google Scholar
• Ikeda , N. and Watanabe , S. 1989 . Stochastic Differential Equations and Diffusion Processes Singapore : North-Holland Mathematical Library 24 – North Holland Publishing Co. .
   Google Scholar
• Kavian , O. 1987 . A remark on the blowing-up of solutions for the Cauchy problem for nonlinear Schrödinger equation . Trans. Am. Math. Soc. , 299 : 193 – 203 .
   Web of Science ®Google Scholar
• Kuksin , S.B. 1999 . Spectral properties of solutions for nonlinear PDES in the turbulent regime . Geometric Funct. Anal. , 9 ( 1 ) : 141 – 184 . [CROSSREF]
   Web of Science ®Google Scholar
• Sulem , C. and Sulem , P.L. 1999 . The Non Linear Schrödinger Equation , Appli. Math. Sci. Vol. 139 , New York , , Singapore : Springer–Verlag .
   Google Scholar
• Weissler , F.B. 1980 . Local existence and nonexistence for semilinear parabolic equations in L p . Indiana Univ. Math. J. , 29 ( 1 ) : 79 – 102 .
   Web of Science ®Google Scholar
• Zakharov , V.E. 1972 . Collapse of Langmuir waves . Soviet Phys. JETP , 1 : 808 – 914 .
   Google Scholar