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Original Articles

Linear wave systems on n-D spatial domains

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Pages 1063-1077 | Received 08 May 2014, Accepted 26 Nov 2014, Published online: 08 Jan 2015

References

  • Aalto, A., Lukkari, T., & Malinen, J. (2014). Acoustic wave guides as infinite-dimensional dynamical systems. Retrieved from http://dx.doi.org/10.1051/cocv/2014019
  • Adams, R.A., & Fournier, J.J.F. (2003). Sobolev spaces, (Vol. 140, 2nd ed.). Amsterdam: Elsevier/Academic Press. ISBN 0-12-044143-8.
  • Arlinskiĭ, Y. (2012). Boundary triplets and maximal accretive extensions of sectorial operators. In S. Hassi, H.S.V. de Snoo, F.H. Szafraniec (Eds.), Operator methods for boundary value problems (Vol. 404, pp. 35–72). Cambridge: Cambridge University Press.
  • Derkach, V.A., Hassi, S., Malamud, M.M., & de Snoo, H. (2009). Boundary relations and generalized resolvents of symmetric operators. Russian Journal of Mathematical Physics, 16(1), 17–60. ISSN 1061-9208.
  • Girault, V., & Raviart, P.-A. (1986). Finite element methods for Navier-Stokes equations: Theory and algorithms (Vol. 5). Berlin: Springer-Verlag. ISBN 3-540-15796-4.
  • Gorbachuk, V.I., & Gorbachuk, M.L. (1991). Boundary value problems for operator differential equations (Vol. 48). Dordrecht: Kluwer Academic Publishers Group. ISBN 0-7923-0381-4. Russian.
  • Grisvard, P. (1985). Elliptic problems in nonsmooth domains (Vol. 24). Boston, MA: Pitman (Advanced Publishing Program). ISBN 0-273-08647-2.
  • Jacob, B., & Zwart, H. (2012). Linear port-Hamiltonian systems on infinite-dimensional spaces (Vol. 223). Basel, Switzerland: Birkhäuser-Verlag.
  • Kurula, M., & Zwart, H. (2012, October). The duality between the gradient and divergence operators on bounded Lipschitz domains. Enschede: Department of Applied Mathematics, University of Twente.
  • Le Gorrec, Y., Zwart, H., & Maschke, B. (2005). Dirac structures and boundary control systems associated with skew-symmetric differential operators. SIAM Journal on Control and Optimization, 44(5), 1864–1892.
  • Lions, J.-L., & Magenes, E. (1972). Non-homogeneous boundary value problems and applications (Vol. I). New York, NY: Springer-Verlag.
  • Malinen, J., & Staffans, O.J. (2006). Conservative boundary control systems. Journal of Differential Equations, 231, 290–312.
  • Malinen, J., & Staffans, O.J. (2007). Impedance passive and conservative boundary control systems. Complex Analysis and Operator Theory, 1, 279–230.
  • Nečas, J. (2012). Direct methods in the theory of elliptic partial differential equations. Heidelberg Berlin: Springer Verlag.
  • Pazy, A. (1983). Semi-groups of linear operators and applications to partial differential equations. Berlin: Springer-Verlag.
  • Renardy, M., & Rogers, R.C. (1993). An introduction to partial differential equations (Vol. 13). New York, NY: Springer-Verlag. ISBN 0-387-97952-2.
  • Spivak, M. (1965). Calculus on manifolds. A modern approach to classical theorems of advanced calculus. New York, NY: W.A. Benjamin, Incorporation.
  • Staffans, O.J., & Weiss, G. (2012). A physically motivated class of scattering passive linear systems. SIAM Journal on Control and Optimization, 50(5), 3083–3112.
  • Trostorff, S. (2013). Autonomous evolutionary inclusions with applications to problems with nonlinear boundary conditions. International Journal of Pure and Applied Mathematics, 85(2), 303–338. ISSN 1314-3395. Retrieved from http://dx.doi.org/10.12732/ijpam.v85i2.10
  • Trostorff, S. (2014). A characterization of boundary conditions yielding maximal monotone operators. Journal of Functional Analysis. Retrieved from http://dx.doi.org/10.1016/j.jfa.2014.08.009
  • Tucsnak, M., and Weiss, G. (2009). Observation and control for operator semigroups. Basel: Birkhäuser Verlag. ISBN 978-3-7643-8993-2. Retrieved from http://dx.doi.org/10.1007/978-3-7643-8994-9
  • Weiss, G., & Staffans, O.J. (2013). Maxwell’s equations as a scattering passive linear system. SIAM Journal on Control and Optimization, 51(5), 3722–3756. ISSN 0363-0129. Retrieved from http://dx.doi.org/10.1137/120869444
  • Yosida, K. (1995). Functional analysis. Classics in Mathematics. Berlin: Springer-Verlag. ISBN 3-540-58654-7. Reprint of the sixth (1980) edition.

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