# American Institute of Mathematical Sciences

• Previous Article
A remark on multiplicity of positive solutions for a class of quasilinear elliptic systems
• PROC Home
• This Issue
• Next Article
Exponential growth in the solution of an affine stochastic differential equation with an average functional and financial market bubbles
2011, 2011(Special): 102-111. doi: 10.3934/proc.2011.2011.102

## Explicit transport semigroup associated to abstract boundary conditions

 1 Universitá degli Studi di Udine, 33100 Udine, Italy

Received  July 2010 Revised  June 2011 Published  October 2011

The linear transport operator associated with abstract bounded boundary conditions, $T_H$, is considered. It is shown that, in some particular cases, a convergent series similar to Dyson-Phillips series can be defined. Sufficient conditions assuring that the sum of this series is a C$_o$-semigroup generated by $T_H$ itself are given.
Citation: Luisa Arlotti. Explicit transport semigroup associated to abstract boundary conditions. Conference Publications, 2011, 2011 (Special) : 102-111. doi: 10.3934/proc.2011.2011.102
 [1] Luisa Arlotti, Bertrand Lods. Transport semigroup associated to positive boundary conditions of unit norm: A Dyson-Phillips approach. Discrete & Continuous Dynamical Systems - B, 2014, 19 (9) : 2739-2766. doi: 10.3934/dcdsb.2014.19.2739 [2] Gabriella Di Blasio. Ultraparabolic equations with nonlocal delayed boundary conditions. Discrete & Continuous Dynamical Systems - A, 2013, 33 (11&12) : 4945-4965. doi: 10.3934/dcds.2013.33.4945 [3] Lahcen Maniar, Martin Meyries, Roland Schnaubelt. Null controllability for parabolic equations with dynamic boundary conditions. Evolution Equations & Control Theory, 2017, 6 (3) : 381-407. doi: 10.3934/eect.2017020 [4] Xiaoyu Fu. Stabilization of hyperbolic equations with mixed boundary conditions. Mathematical Control & Related Fields, 2015, 5 (4) : 761-780. doi: 10.3934/mcrf.2015.5.761 [5] Gennaro Infante. Positive solutions of differential equations with nonlinear boundary conditions. Conference Publications, 2003, 2003 (Special) : 432-438. doi: 10.3934/proc.2003.2003.432 [6] V. Casarino, K.-J. Engel, G. Nickel, S. Piazzera. Decoupling techniques for wave equations with dynamic boundary conditions. Discrete & Continuous Dynamical Systems - A, 2005, 12 (4) : 761-772. doi: 10.3934/dcds.2005.12.761 [7] Madalina Petcu, Roger Temam. The one dimensional shallow water equations with Dirichlet boundary conditions on the velocity. Discrete & Continuous Dynamical Systems - S, 2011, 4 (1) : 209-222. doi: 10.3934/dcdss.2011.4.209 [8] Dagny Butler, Eunkyung Ko, Eun Kyoung Lee, R. Shivaji. Positive radial solutions for elliptic equations on exterior domains with nonlinear boundary conditions. Communications on Pure & Applied Analysis, 2014, 13 (6) : 2713-2731. doi: 10.3934/cpaa.2014.13.2713 [9] Zhenhua Zhang. Asymptotic behavior of solutions to the phase-field equations with neumann boundary conditions. Communications on Pure & Applied Analysis, 2005, 4 (3) : 683-693. doi: 10.3934/cpaa.2005.4.683 [10] Jinju Xu. A new proof of gradient estimates for mean curvature equations with oblique boundary conditions. Communications on Pure & Applied Analysis, 2016, 15 (5) : 1719-1742. doi: 10.3934/cpaa.2016010 [11] Chérif Amrouche, Nour El Houda Seloula. $L^p$-theory for the Navier-Stokes equations with pressure boundary conditions. Discrete & Continuous Dynamical Systems - S, 2013, 6 (5) : 1113-1137. doi: 10.3934/dcdss.2013.6.1113 [12] Giuseppe Da Prato, Alessandra Lunardi. On a class of elliptic and parabolic equations in convex domains without boundary conditions. Discrete & Continuous Dynamical Systems - A, 2008, 22 (4) : 933-953. doi: 10.3934/dcds.2008.22.933 [13] Shu Luan. On the existence of optimal control for semilinear elliptic equations with nonlinear neumann boundary conditions. Mathematical Control & Related Fields, 2017, 7 (3) : 493-506. doi: 10.3934/mcrf.2017018 [14] Zhongkai Guo. Invariant foliations for stochastic partial differential equations with dynamic boundary conditions. Discrete & Continuous Dynamical Systems - A, 2015, 35 (11) : 5203-5219. doi: 10.3934/dcds.2015.35.5203 [15] Ciprian G. Gal, Mahamadi Warma. Elliptic and parabolic equations with fractional diffusion and dynamic boundary conditions. Evolution Equations & Control Theory, 2016, 5 (1) : 61-103. doi: 10.3934/eect.2016.5.61 [16] Laurence Cherfils, Madalina Petcu. On the viscous Cahn-Hilliard-Navier-Stokes equations with dynamic boundary conditions. Communications on Pure & Applied Analysis, 2016, 15 (4) : 1419-1449. doi: 10.3934/cpaa.2016.15.1419 [17] Mahamadi Warma. Semi linear parabolic equations with nonlinear general Wentzell boundary conditions. Discrete & Continuous Dynamical Systems - A, 2013, 33 (11&12) : 5493-5506. doi: 10.3934/dcds.2013.33.5493 [18] Jason Metcalfe, Jacob Perry. Global solutions to quasilinear wave equations in homogeneous waveguides with Neumann boundary conditions. Communications on Pure & Applied Analysis, 2012, 11 (2) : 547-556. doi: 10.3934/cpaa.2012.11.547 [19] B. Abdellaoui, E. Colorado, I. Peral. Existence and nonexistence results for a class of parabolic equations with mixed boundary conditions. Communications on Pure & Applied Analysis, 2006, 5 (1) : 29-54. doi: 10.3934/cpaa.2006.5.29 [20] Boris Muha, Zvonimir Tutek. Note on evolutionary free piston problem for Stokes equations with slip boundary conditions. Communications on Pure & Applied Analysis, 2014, 13 (4) : 1629-1639. doi: 10.3934/cpaa.2014.13.1629

Impact Factor: