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Volumn 22, Issue 6, 2004, Pages 1421-1486

Non-random invariant sets for some systems of parabolic stochastic partial differential equations

Author keywords

Comparison principle; Invariant sets; Stochastic parabolic systems; Wong Zaka approximations

Indexed keywords


EID: 8344259011     PISSN: 07362994     EISSN: None     Source Type: Journal    
DOI: 10.1081/SAP-200029487     Document Type: Article
Times cited : (16)

References (59)
  • 1
    • 36049058276 scopus 로고
    • Time variation of the Ginzburg-Landau order parameter
    • Abrahams, E.; Tsuneto, T. Time variation of the Ginzburg-Landau order parameter. Phys. Rev. 1966, 152 (1), 416-432.
    • (1966) Phys. Rev. , vol.152 , Issue.1 , pp. 416-432
    • Abrahams, E.1    Tsuneto, T.2
  • 2
    • 0001351033 scopus 로고
    • Invariant sets and existence theorems for semilinear parabolic and elliptic systems
    • Amann, H. Invariant sets and existence theorems for semilinear parabolic and elliptic systems. J. Math. Anal Appl. 1978, 65, 432-467.
    • (1978) J. Math. Anal Appl. , vol.65 , pp. 432-467
    • Amann, H.1
  • 3
    • 0001835099 scopus 로고
    • Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems
    • Schmeisser, H.-J., Tribel, H., Eds.; Teubner Verlag: Stuttgart-Leipzig
    • Amann, H. Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems. In Function Spaces, Differential Operators and Nonlinear Analysis; Schmeisser, H.-J., Tribel, H., Eds.; Teubner Verlag: Stuttgart-Leipzig, 1993; 9-126.
    • (1993) Function Spaces, Differential Operators and Nonlinear Analysis , pp. 9-126
    • Amann, H.1
  • 5
    • 0032165082 scopus 로고    scopus 로고
    • Order-preserving random dynamical systems: Equilibria, attractors, applications
    • Arnold, L.; Chueshov, I.D. Order-preserving random dynamical systems: Equilibria, attractors, applications. Dyn. Stab. Syst. 1998, 13, 265-280.
    • (1998) Dyn. Stab. Syst. , vol.13 , pp. 265-280
    • Arnold, L.1    Chueshov, I.D.2
  • 6
    • 0037933463 scopus 로고    scopus 로고
    • Comparison of systems of stochastic partial differential equations
    • Assing, S. Comparison of systems of stochastic partial differential equations. Stochastic Processes Appl. 1999, 82, 259-282.
    • (1999) Stochastic Processes Appl. , vol.82 , pp. 259-282
    • Assing, S.1
  • 7
    • 15444362058 scopus 로고    scopus 로고
    • The viability theorem for stochastic differential inclusions
    • Aubin, J.P.; Da Prato, G. The viability theorem for stochastic differential inclusions. Stoch. Anal. Appl. 1998, 16, 1-15.
    • (1998) Stoch. Anal. Appl. , vol.16 , pp. 1-15
    • Aubin, J.P.1    Da Prato, G.2
  • 11
    • 0001181333 scopus 로고    scopus 로고
    • On the behavior of solutions to certain parabolic SPDE's driven by Wiener processes
    • Bergé, B.; Chueshov, I.D.; Vuillermot, P.-A. On the behavior of solutions to certain parabolic SPDE's driven by Wiener processes. Stochastic Processes Appl. 2001, 92, 237-263.
    • (2001) Stochastic Processes Appl. , vol.92 , pp. 237-263
    • Bergé, B.1    Chueshov, I.D.2    Vuillermot, P.-A.3
  • 13
    • 0032135817 scopus 로고    scopus 로고
    • Large-time asymptotic equivalence for a class of non autonomous semilinear parabolic equations
    • Bernfeld, S.R.; Hu, Y.Y.; Vuillermot, P.-A. Large-time asymptotic equivalence for a class of non autonomous semilinear parabolic equations. Bull. Sci. Math. 1998, 722 (5), 337-368.
    • (1998) Bull. Sci. Math. , vol.722 , Issue.5 , pp. 337-368
    • Bernfeld, S.R.1    Hu, Y.Y.2    Vuillermot, P.-A.3
  • 14
    • 0039740083 scopus 로고
    • A convergence result for stochastic partial differential equations
    • Brzeźniak, Z.; Capiński, M.; Flandoli, F. A convergence result for stochastic partial differential equations. Stochastics 1988, 24, 423-445.
    • (1988) Stochastics , vol.24 , pp. 423-445
    • Brzeźniak, Z.1    Capiński, M.2    Flandoli, F.3
  • 16
    • 0038270631 scopus 로고    scopus 로고
    • Stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term
    • Cerrai, S. Stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term. Probab. Theory Relat. Fields 2003, 125, 271-304.
    • (2003) Probab. Theory Relat. Fields , vol.125 , pp. 271-304
    • Cerrai, S.1
  • 17
    • 0000805398 scopus 로고
    • Positively invariant regions for systems of nonlinear diffusion equations
    • Chueh, K.N.; Conley, C.C.; Smoller, J.A. Positively invariant regions for systems of nonlinear diffusion equations. Indiana Univ. Math. J. 1977, 26, 373-392.
    • (1977) Indiana Univ. Math. J. , vol.26 , pp. 373-392
    • Chueh, K.N.1    Conley, C.C.2    Smoller, J.A.3
  • 18
    • 84876892179 scopus 로고    scopus 로고
    • Order-preserving random dynamical systems generated by a class of coupled stochastic semilinear parabolic equations
    • Berlin, Aug 1-7; Fiedler, B., Gröger, K., Sprekels, J., Eds.; World Scientific: Singapore
    • Chueshov, I.D. Order-preserving random dynamical systems generated by a class of coupled stochastic semilinear parabolic equations International Conference on Differential Equations, EQUADIF 99, Berlin, Aug 1-7, 1999; Fiedler, B., Gröger, K., Sprekels, J., Eds.; World Scientific: Singapore, 2000; Vol. 1, 711-716.
    • (1999) International Conference on Differential Equations, EQUADIF 99 , vol.1 , pp. 711-716
    • Chueshov, I.D.1
  • 21
    • 0001331899 scopus 로고    scopus 로고
    • Long-time behavior of solutions to a class of quasilinear parabolic equations with random coefficients
    • Chueshov, I.D.; Vuillermot, P.-A. Long-time behavior of solutions to a class of quasilinear parabolic equations with random coefficients. Ann. I. H. Poincaré-AN 1998, 15 (2), 191-232.
    • (1998) Ann. I. H. Poincaré-AN , vol.15 , Issue.2 , pp. 191-232
    • Chueshov, I.D.1    Vuillermot, P.-A.2
  • 22
    • 0032187776 scopus 로고    scopus 로고
    • Long-time behavior of solutions to a class of stochastic parabolic equations with homogeneous white noise: Stratonovitch's case
    • Chueshov, I.D.; Vuillermot, P.-A. Long-time behavior of solutions to a class of stochastic parabolic equations with homogeneous white noise: Stratonovitch's case. Probab. Theory Relat. Fields 1998, 112, 149-202.
    • (1998) Probab. Theory Relat. Fields , vol.112 , pp. 149-202
    • Chueshov, I.D.1    Vuillermot, P.-A.2
  • 23
    • 0034342828 scopus 로고    scopus 로고
    • Long-time behavior of solutions to a class of stochastic parabolic equations with homogeneous white noise: Itô's case
    • Chueshov, I.D.; Vuillermot, P.-A. Long-time behavior of solutions to a class of stochastic parabolic equations with homogeneous white noise: Itô's case. Stochastic Anal. and Appl. 2000, 18 (4), 581-615.
    • (2000) Stochastic Anal. and Appl. , vol.18 , Issue.4 , pp. 581-615
    • Chueshov, I.D.1    Vuillermot, P.-A.2
  • 24
    • 8344271628 scopus 로고    scopus 로고
    • Parabolic stochastic partial differential equations with dynamical boundary conditions
    • Chueshov, I.D.; Schmalfuss, B. Parabolic stochastic partial differential equations with dynamical boundary conditions. Differential and Integral Equations. 2004, 17 (7-8), 751-780.
    • (2004) Differential and Integral Equations , vol.17 , Issue.7-8 , pp. 751-780
    • Chueshov, I.D.1    Schmalfuss, B.2
  • 29
    • 0000630747 scopus 로고
    • Comparison principles for reaction-diffusion systems: Irregular comparison functions and applications to questions of stability and speed of propagation of disturbances
    • Fife, P.C.; Tang, M.M. Comparison principles for reaction-diffusion systems: Irregular comparison functions and applications to questions of stability and speed of propagation of disturbances. J. Diff. Eqs. 1981, 40, 168-185.
    • (1981) J. Diff. Eqs. , vol.40 , pp. 168-185
    • Fife, P.C.1    Tang, M.M.2
  • 30
    • 0039043021 scopus 로고
    • Comparison theorems for stochastic differential equations in finite and infinite dimensions
    • Geiss, C.; Manthey, R. Comparison theorems for stochastic differential equations in finite and infinite dimensions. Stochastic Processes Appl. 1994, 53, 23-35.
    • (1994) Stochastic Processes Appl. , vol.53 , pp. 23-35
    • Geiss, C.1    Manthey, R.2
  • 32
    • 0040176065 scopus 로고
    • On the approximation of stochastic partial differential equations. Part I
    • Gyöngy, I. On the approximation of stochastic partial differential equations. Part I. Stochastics 1988, 25, 59-85.
    • (1988) Stochastics , vol.25 , pp. 59-85
    • Gyöngy, I.1
  • 33
    • 33846785362 scopus 로고
    • On the approximation of stochastic partial differential equations. Part II
    • Gyöngy, I. On the approximation of stochastic partial differential equations. Part II. Stochastics 1989, 26, 129-164.
    • (1989) Stochastics , vol.26 , pp. 129-164
    • Gyöngy, I.1
  • 34
    • 0003744101 scopus 로고
    • AMS-Mathematical Surveys and Monographs 25; American Mathematical Society: Providence
    • Hale, J.K. Asymptotic Behavior of Dissipative Systems, AMS-Mathematical Surveys and Monographs 25; American Mathematical Society: Providence, 1988.
    • (1988) Asymptotic Behavior of Dissipative Systems
    • Hale, J.K.1
  • 35
    • 0003461830 scopus 로고
    • Pitman Research Notes in Mathematics Series 247; Longman Science and Technology: Harlow
    • Hess, P. Periodic-Parabolic Boundary Value Problems and Positivity, Pitman Research Notes in Mathematics Series 247; Longman Science and Technology: Harlow, 1991.
    • (1991) Periodic-Parabolic Boundary Value Problems and Positivity
    • Hess, P.1
  • 36
    • 0013356601 scopus 로고    scopus 로고
    • Asymptotic behavior of positive solutions of random and stochastic parabolic equations of Fisher and Kolmogorov types
    • Hetzer, G.; Shen, W.; Zhu, S. Asymptotic behavior of positive solutions of random and stochastic parabolic equations of Fisher and Kolmogorov types. J. Dyn. Diff. Equations 2002, 14, 139-188.
    • (2002) J. Dyn. Diff. Equations , vol.14 , pp. 139-188
    • Hetzer, G.1    Shen, W.2    Zhu, S.3
  • 38
    • 0002465954 scopus 로고
    • Comparison methods for a class of function valued stochastic partial differential equations
    • Kotelenez, P. Comparison methods for a class of function valued stochastic partial differential equations. Probab. Theory Rel. Fields 1992, 93, 1-19.
    • (1992) Probab. Theory Rel. Fields , vol.93 , pp. 1-19
    • Kotelenez, P.1
  • 40
    • 0031476783 scopus 로고    scopus 로고
    • Invariance for stochastic equations with regular coefficients
    • Milian, A. Invariance for stochastic equations with regular coefficients. Stochastic Anal. Appl. 1997, 15, 91-101.
    • (1997) Stochastic Anal. Appl. , vol.15 , pp. 91-101
    • Milian, A.1
  • 43
    • 0002012917 scopus 로고
    • Approximations of solutions of stochastic differential equations driven by semi-martingales
    • Protter, P. Approximations of solutions of stochastic differential equations driven by semi-martingales. Ann. Prob. 1985, 13 (3), 716-743.
    • (1985) Ann. Prob. , vol.13 , Issue.3 , pp. 716-743
    • Protter, P.1
  • 44
    • 38249040330 scopus 로고
    • Compactness results for time-dependent parabolic systems
    • Redlinger, R. Compactness results for time-dependent parabolic systems. J. Diff. Eqs. 1986, 64, 133-153.
    • (1986) J. Diff. Eqs. , vol.64 , pp. 133-153
    • Redlinger, R.1
  • 45
    • 0017630393 scopus 로고
    • Invariant sets for systems of partial differential equations I. Parabolic equations
    • Redheffer, R.; Walter, W. Invariant sets for systems of partial differential equations I. parabolic equations. Arch. Rat. Mech. Anal. 1978, 67, 41-52.
    • (1978) Arch. Rat. Mech. Anal. , vol.67 , pp. 41-52
    • Redheffer, R.1    Walter, W.2
  • 46
    • 0037986125 scopus 로고    scopus 로고
    • Hölder-Sobolev regularity of solutions to a class of SPDE's driven by a spatially colored noise
    • Sanz-Solé, M.; Vuillemot, P.-A. Hölder-Sobolev regularity of solutions to a class of SPDE's driven by a spatially colored noise. C. R. Acad. Sci. Paris, Ser. I 2002, 334, 869-874.
    • (2002) C. R. Acad. Sci. Paris, Ser. I , vol.334 , pp. 869-874
    • Sanz-Solé, M.1    Vuillemot, P.-A.2
  • 47
    • 0037567625 scopus 로고    scopus 로고
    • Equivalence and Hölder-Sobolev regularity of solutions for a class of non autonomous stochastic partial differential equations
    • Sanz-Solé, M.; Vuillermot, P.-A. Equivalence and Hölder-Sobolev regularity of solutions for a class of non autonomous stochastic partial differential equations. Ann. I. H. Poincaré-PR 2003, 39, 703-742.
    • (2003) Ann. I. H. Poincaré-PR , vol.39 , pp. 703-742
    • Sanz-Solé, M.1    Vuillermot, P.-A.2
  • 53
    • 21844495273 scopus 로고
    • Approximation theorem of Wong-Zakai type for nonlinear stochastic partial differential equations
    • Twardowska, K. Approximation theorem of Wong-Zakai type for nonlinear stochastic partial differential equations. Stoch. Anal. Appl. 1995, 13, 601-626.
    • (1995) Stoch. Anal. Appl. , vol.13 , pp. 601-626
    • Twardowska, K.1
  • 54
    • 0001011978 scopus 로고    scopus 로고
    • Wong-Zakaï approximations for stochastic differential equations
    • Twardowska, K. Wong-Zakaï approximations for stochastic differential equations. Acta Applic. Math. 1996, 43, 317-359.
    • (1996) Acta Applic. Math. , vol.43 , pp. 317-359
    • Twardowska, K.1
  • 55
    • 0002283608 scopus 로고
    • Stabilization of solutions of weakly coupled cooperative parabolic systems
    • Vishnevskiǐ, M.P. Stabilization of solutions of weakly coupled cooperative parabolic systems (Russian). Mat. Sb. 1992, 183 (10), 45-62.
    • (1992) Mat. Sb. , vol.183 , Issue.10 , pp. 45-62
    • Vishnevskiǐ, M.P.1
  • 59
    • 8344268966 scopus 로고    scopus 로고
    • Stochastic invariance and consistency of financial models
    • Zabczyk, J. Stochastic invariance and consistency of financial models. Rendiconti Mat. Acc. Lincei 2000, 9, 67-80.
    • (2000) Rendiconti Mat. Acc. Lincei , vol.9 , pp. 67-80
    • Zabczyk, J.1


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