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.
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     title = {Stability of semilinear equations with boundary and pointwise noise},
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     pages = {55--93},
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     zbl = {0830.60056},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1995_4_22_1_55_0/}
}
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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] H. Amann, On abstract parabolic fundamental solutions. J. Math. Soc. Japan 39 (1987), 93-116. | MR | Zbl

[2] A.V. Balakrishnan, Applied Functional Analysis. Springer-Verlag, New York 1976. | MR | Zbl

[3] L. Arnold - R.F. Curtain - P. Kotelenez, Nonlinear stochastic evolution equations in Hilbert space. Report no. 17, Forschungsschwerpunkt Dynamische Systeme, Universität Bremen (1980).

[4] R. Arima, On general boundary value problem for parabolic equations. J. Math. Kyoto Univ. 4 (1964), 207-243. | MR | Zbl

[5] S. Chen - R. Triggiani, Proof of extensions of two conjectures on structural damping for elastic systems. Pacific J. Math. 136 (1989), 15-55. | MR | Zbl

[6] S. Chen - R. Triggiani, Characterizations of domains of fractional powers of certain operators arising in elastic systems. J. Differential Equations 88 (1990), 279-293. | MR | Zbl

[7] R. Datko, Extending a theorem of A.M. Liapunov to Hilbert space. J. Math. Analysis Appl. 32 (1970), 610-616. | MR | Zbl

[8] G. Da Prato - J. Zabczyk, Stochastic Equations in Infinite Dimensions. Cambridge Univ. Press, Cambridge (1992). | MR | Zbl

[9] G. Da Prato - J. Zabczyk, Evolution equations with white-noise boundary conditions. Stochastics Stochastics Rep. 42 (1993), 167-182. | MR | Zbl

[10] G. Da Prato - D.G. Atarek - J. Zabczyk, Invariant measures for semilinear stochastic equations. Stochastic Anal. Appl. 10 (1992), 387-408. | MR | Zbl

[11] T.E. Duncan - B. Maslowski - B. Pasik-Duncan, Adaptive boundary and point control of linear stochastic distributed parameter systems. SIAM J. on Control and Optim. 32 (1994), 648-672. | MR | Zbl

[12] D.E. Edmunds - H. Triebel, Entropy numbers and approximation numbers in function spaces. Proc. London Math. Soc. 58 (1989), 137-152. | MR | Zbl

[13] F. Flandoli, 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 | Zbl

[14] F. Flandoli, Dirichlet boundary value problem for stochastic parabolic equations: compatibility relations and regularity of solutions. Stochastics Stochastics Rep. 29 (1990), 331-357. | MR | Zbl

[15] F. Flandoli, On the semigroup approach to stochastic evolution equations. Stochastic Anal. Appl. 10 (1992), 181-203. | MR | Zbl

[16] I.C. Gokhberg - M.G. Krein, Introduction to the Theory of Linear Non-selfadjoint Operators. Nauka, Moscow (1965), Russian (English translation AMS, Providence, 1969). | Zbl

[17] A. Ichikawa, Stability of semilinear stochastic evolution equations. J. Math. Anal. Appl. 90 (1982), 12-44. | MR | Zbl

[18] A. Ichikawa, Semilinear stochastic evolution equations: boundedness, stability and invariant measures. Stochastics 12 (1984), 1-39. | MR | Zbl

[19] A. Ichikawa, Equivalence of Lp stability and exponential stability for a class of nonlinear semigroups. Nonlinear Analysis 8 (1984), 805-815. | MR | Zbl

[20] A. Ichikawa, 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

[21] A. Ichikawa, 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 | Zbl

[22] I. Lasiecka - R. Triggiani, Feedback semigroups and cosine operators for boundary feedback parabolic and hyperbolic equations. J. Differential Eq.'s 47 (1983), 246-272. | MR

[23] I. Lasiecka, Unified theory of abstract parabolic boundary value problems: A semigroup approach. Appl. Math. Optim. 6 (1980), 281-333. | MR | Zbl

[24] I. Lasiecka - R. Triggiani, Numerical approximations of algebraic Riccati equations modelled by analytic semigroups and applications. Math. Computation 57 (1991), 639-662 and S 13-S37. | MR | Zbl

[25] J.L. Lions - E. Magenes, Nonhomogeneous Boundary Value Problems and Applications I. Springer-Verlag, Berlin (1972). | Zbl

[26] R. Manthey - B. Maslowski, Qualitative behavior of solutions of stochastic reaction-diffusion equations. Stochastic Processes Appl. 37 (1992), 256-289. | MR | Zbl

[27] X. Mao - L. Marcus, Wave equation with stochastic boundary values. J. Math. Anal. Appl. 177 (1993), 315-341. | MR | Zbl

[28] B. Maslowski, Uniqueness and stability of invariant measures for stochastic differential equations in Hilbert spaces. Stochastics Stochastics Rep. 28 (1989), 85-114. | MR | Zbl

[29] J. Seidler, Da Prato-Zabczyk's maximal inequality revisited I. Mathematica Bohemica 118 (1993), 67-106. | MR | Zbl

[30] R.B. Sowers, New asymptotic results for stochastic partial differential equations. Ph.D. Dissertation, University of Maryland.

[31] R.B. Sowers, Multidimensional reaction-diffusion equations with white noise boundary perturbations. Annals of Probability, to appear. | MR | Zbl

[32] I Vrkoč, A dynamical system in a Hilbert space with a weakly attractive nonstationary point. Mathematica Bohemica 118 (1993), 401-423. | MR | Zbl

[33] J. Zabczyk, On decomposition of generators. SIAM J. Control Optimiz. 16 (1978), 523-534. | MR | Zbl