# American Institute of Mathematical Sciences

February  2004, 10(1&2): 177-192. doi: 10.3934/dcds.2004.10.177

## Transition semigroups corresponding to Lipschitz dissipative systems

 1 Scuola Normale Superiore di Pisa, Piazza dei Cavalieri 7, 56126, Pisa, Italy

Received  July 2001 Revised  February 2002 Published  October 2003

We consider a semilinear differential stochastic equation in a Hilbert space $H$ with a dissipative and Lipschitz nonlinearity. We study the corresponding transition semigroup in a space $L^2(H,\nu)$ where $\nu$ is an invariant measure.
Citation: Giuseppe Da Prato. Transition semigroups corresponding to Lipschitz dissipative systems. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 177-192. doi: 10.3934/dcds.2004.10.177
 [1] Fritz Colonius, Marco Spadini. Fundamental semigroups for dynamical systems. Discrete and Continuous Dynamical Systems, 2006, 14 (3) : 447-463. doi: 10.3934/dcds.2006.14.447 [2] Jin Zhang, Peter E. Kloeden, Meihua Yang, Chengkui Zhong. Global exponential κ-dissipative semigroups and exponential attraction. Discrete and Continuous Dynamical Systems, 2017, 37 (6) : 3487-3502. doi: 10.3934/dcds.2017148 [3] Sebastián Donoso. Enveloping semigroups of systems of order d. Discrete and Continuous Dynamical Systems, 2014, 34 (7) : 2729-2740. doi: 10.3934/dcds.2014.34.2729 [4] Katarzyna Pichór, Ryszard Rudnicki. Applications of stochastic semigroups to cell cycle models. Discrete and Continuous Dynamical Systems - B, 2019, 24 (5) : 2365-2381. doi: 10.3934/dcdsb.2019099 [5] Katarzyna PichÓr, Ryszard Rudnicki. Stability of stochastic semigroups and applications to Stein's neuronal model. Discrete and Continuous Dynamical Systems - B, 2018, 23 (1) : 377-385. doi: 10.3934/dcdsb.2018026 [6] Everaldo de Mello Bonotto, Matheus Cheque Bortolan, Rodolfo Collegari, José Manuel Uzal. Impulses in driving semigroups of nonautonomous dynamical systems: Application to cascade systems. Discrete and Continuous Dynamical Systems - B, 2021, 26 (9) : 4645-4661. doi: 10.3934/dcdsb.2020306 [7] Angela A. Albanese, Elisabetta M. Mangino. Analytic semigroups and some degenerate evolution equations defined on domains with corners. Discrete and Continuous Dynamical Systems, 2015, 35 (2) : 595-615. doi: 10.3934/dcds.2015.35.595 [8] Alexandre Nolasco de Carvalho, Jan W. Cholewa, Tomasz Dlotko. Damped wave equations with fast growing dissipative nonlinearities. Discrete and Continuous Dynamical Systems, 2009, 24 (4) : 1147-1165. doi: 10.3934/dcds.2009.24.1147 [9] Alastair Fletcher. Quasiregular semigroups with examples. Discrete and Continuous Dynamical Systems, 2019, 39 (4) : 2157-2172. doi: 10.3934/dcds.2019090 [10] José A. Conejero, Alfredo Peris. Chaotic translation semigroups. Conference Publications, 2007, 2007 (Special) : 269-276. doi: 10.3934/proc.2007.2007.269 [11] Min He. On continuity in parameters of integrated semigroups. Conference Publications, 2003, 2003 (Special) : 403-412. doi: 10.3934/proc.2003.2003.403 [12] Edmond W. H. Lee. Equational theories of unstable involution semigroups. Electronic Research Announcements, 2017, 24: 10-20. doi: 10.3934/era.2017.24.002 [13] Yuri Latushkin, Valerian Yurov. Stability estimates for semigroups on Banach spaces. Discrete and Continuous Dynamical Systems, 2013, 33 (11&12) : 5203-5216. doi: 10.3934/dcds.2013.33.5203 [14] Jeremy LeCrone, Gieri Simonett. Continuous maximal regularity and analytic semigroups. Conference Publications, 2011, 2011 (Special) : 963-970. doi: 10.3934/proc.2011.2011.963 [15] Samir EL Mourchid. On a hypercylicity criterion for strongly continuous semigroups. Discrete and Continuous Dynamical Systems, 2005, 13 (2) : 271-275. doi: 10.3934/dcds.2005.13.271 [16] Delio Mugnolo, Abdelaziz Rhandi. Ornstein–Uhlenbeck semigroups on star graphs. Discrete and Continuous Dynamical Systems - S, 2022  doi: 10.3934/dcdss.2022030 [17] Alexandre N. Carvalho, José A. Langa, James C. Robinson. Forwards dynamics of non-autonomous dynamical systems: Driving semigroups without backwards uniqueness and structure of the attractor. Communications on Pure and Applied Analysis, 2020, 19 (4) : 1997-2013. doi: 10.3934/cpaa.2020088 [18] Nakao Hayashi, Pavel I. Naumkin. Modified wave operator for Schrodinger type equations with subcritical dissipative nonlinearities. Inverse Problems and Imaging, 2007, 1 (2) : 391-398. doi: 10.3934/ipi.2007.1.391 [19] Chao Wang, Ravi P Agarwal. Almost automorphic functions on semigroups induced by complete-closed time scales and application to dynamic equations. Discrete and Continuous Dynamical Systems - B, 2020, 25 (2) : 781-798. doi: 10.3934/dcdsb.2019267 [20] Luigi C. Berselli, Franco Flandoli. Remarks on determining projections for stochastic dissipative equations. Discrete and Continuous Dynamical Systems, 1999, 5 (1) : 197-214. doi: 10.3934/dcds.1999.5.197

2020 Impact Factor: 1.392