@article{ASNSP_1995_4_22_1_55_0, author = {Maslowski, Bohdan}, title = {Stability of semilinear equations with boundary and pointwise noise}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, publisher = {Scuola normale superiore}, volume = {Ser. 4, 22}, number = {1}, year = {1995}, pages = {55-93}, zbl = {0830.60056}, mrnumber = {1315350}, language = {en}, url = {http://www.numdam.org/item/ASNSP_1995_4_22_1_55_0} }
Maslowski, Bohdan. Stability of semilinear equations with boundary and pointwise noise. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 22 (1995) no. 1, pp. 55-93. http://www.numdam.org/item/ASNSP_1995_4_22_1_55_0/
[1] On abstract parabolic fundamental solutions. J. Math. Soc. Japan 39 (1987), 93-116. | MR 867989 | Zbl 0616.47032
,[2] Applied Functional Analysis. Springer-Verlag, New York 1976. | MR 470699 | Zbl 0333.93051
,[3] Nonlinear stochastic evolution equations in Hilbert space. Report no. 17, Forschungsschwerpunkt Dynamische Systeme, Universität Bremen (1980).
- - ,[4] On general boundary value problem for parabolic equations. J. Math. Kyoto Univ. 4 (1964), 207-243. | MR 197997 | Zbl 0143.13902
,[5] Proof of extensions of two conjectures on structural damping for elastic systems. Pacific J. Math. 136 (1989), 15-55. | MR 971932 | Zbl 0633.47025
- ,[6] Characterizations of domains of fractional powers of certain operators arising in elastic systems. J. Differential Equations 88 (1990), 279-293. | MR 1081250 | Zbl 0717.34066
- ,[7] Extending a theorem of A.M. Liapunov to Hilbert space. J. Math. Analysis Appl. 32 (1970), 610-616. | MR 268717 | Zbl 0211.16802
,[8] Stochastic Equations in Infinite Dimensions. Cambridge Univ. Press, Cambridge (1992). | MR 1207136 | Zbl 0761.60052
- ,[9] Evolution equations with white-noise boundary conditions. Stochastics Stochastics Rep. 42 (1993), 167-182. | MR 1291187 | Zbl 0814.60055
- ,[10] Invariant measures for semilinear stochastic equations. Stochastic Anal. Appl. 10 (1992), 387-408. | MR 1178482 | Zbl 0758.60057
- - ,[11] Adaptive boundary and point control of linear stochastic distributed parameter systems. SIAM J. on Control and Optim. 32 (1994), 648-672. | MR 1269987 | Zbl 0802.93035
- - ,[12] Entropy numbers and approximation numbers in function spaces. Proc. London Math. Soc. 58 (1989), 137-152. | MR 969551 | Zbl 0629.46034
- ,[13] Direct solution of a Riccati equation arising in a stochatic control problem with control and observations on the boundary. Appl. Math. Optim. 14 (1986), 107-129. | MR 863335 | Zbl 0606.93070
,[14] Dirichlet boundary value problem for stochastic parabolic equations: compatibility relations and regularity of solutions. Stochastics Stochastics Rep. 29 (1990), 331-357. | MR 1042066 | Zbl 0696.60057
,[15] On the semigroup approach to stochastic evolution equations. Stochastic Anal. Appl. 10 (1992), 181-203. | MR 1154534 | Zbl 0762.60046
,[16] Introduction to the Theory of Linear Non-selfadjoint Operators. Nauka, Moscow (1965), Russian (English translation AMS, Providence, 1969). | Zbl 0181.13504
- ,[17] Stability of semilinear stochastic evolution equations. J. Math. Anal. Appl. 90 (1982), 12-44. | MR 680861 | Zbl 0497.93055
,[18] Semilinear stochastic evolution equations: boundedness, stability and invariant measures. Stochastics 12 (1984), 1-39. | MR 738933 | Zbl 0538.60068
,[19] Equivalence of Lp stability and exponential stability for a class of nonlinear semigroups. Nonlinear Analysis 8 (1984), 805-815. | MR 750052 | Zbl 0547.47041
,[20] A semigroup model for parabolic equations with boundary and pointwise noise. Stochastic Space-Time Models and Limit Theorems, D. Reidel Publishing Company (1985), 81-94. | Zbl 0593.60066
,[21] Stability of parabolic equations with boundary and pointwise noise. In "Stochastic Differential Systems" (Proceedings), Lecture Notes in Control and Information Sciences 69, Springer-Verlag, Berlin 1985, 55-66. | MR 798307 | Zbl 0572.93075
,[22] Feedback semigroups and cosine operators for boundary feedback parabolic and hyperbolic equations. J. Differential Eq.'s 47 (1983), 246-272. | MR 688105
- ,[23] Unified theory of abstract parabolic boundary value problems: A semigroup approach. Appl. Math. Optim. 6 (1980), 281-333. | MR 587501 | Zbl 0448.47019
,[24] Numerical approximations of algebraic Riccati equations modelled by analytic semigroups and applications. Math. Computation 57 (1991), 639-662 and S 13-S37. | MR 1094953 | Zbl 0735.65043
- ,[25] Nonhomogeneous Boundary Value Problems and Applications I. Springer-Verlag, Berlin (1972). | Zbl 0223.35039
- ,[26] Qualitative behavior of solutions of stochastic reaction-diffusion equations. Stochastic Processes Appl. 37 (1992), 256-289. | MR 1191151 | Zbl 0761.60055
- ,[27] Wave equation with stochastic boundary values. J. Math. Anal. Appl. 177 (1993), 315-341. | MR 1231485 | Zbl 0784.60061
- ,[28] Uniqueness and stability of invariant measures for stochastic differential equations in Hilbert spaces. Stochastics Stochastics Rep. 28 (1989), 85-114. | MR 1018545 | Zbl 0683.60037
,[29] Da Prato-Zabczyk's maximal inequality revisited I. Mathematica Bohemica 118 (1993), 67-106. | MR 1213834 | Zbl 0785.35115
,[30] New asymptotic results for stochastic partial differential equations. Ph.D. Dissertation, University of Maryland.
,[31] Multidimensional reaction-diffusion equations with white noise boundary perturbations. Annals of Probability, to appear. | MR 1331216 | Zbl 0834.60067
,[32] A dynamical system in a Hilbert space with a weakly attractive nonstationary point. Mathematica Bohemica 118 (1993), 401-423. | MR 1251884 | Zbl 0794.34054
,[33] On decomposition of generators. SIAM J. Control Optimiz. 16 (1978), 523-534. | MR 512915 | Zbl 0393.93023
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