American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Existence of radial solutions for an elliptic problem involving exponential nonlinearities
  • DCDS Home
  • This Issue
  • Next Article
    Schrödinger equations with a spatially decaying nonlinearity: Existence and stability of standing waves
January  2008, 21(1): 187-220. doi: 10.3934/dcds.2008.21.187

Superposition of selfdual functionals in non-homogeneous boundary value problems and differential systems

Nassif Ghoussoub 1,

1. 

Department of Mathematics, The University of British Columbia, Vancouver BC Canada V6T 1Z2

Received  March 2007 Published  February 2008

Selfdual variational theory -- developed in [8] and [9] -- allows for the superposition of appropriate "boundary" Lagrangians with "interior" Lagrangians, leading to a variational formulation and resolution of problems with various linear and nonlinear boundary constraints that are not amenable to standard Euler-Lagrange theory. The superposition of several selfdual Lagrangians is also possible in many natural settings, leading to a variational resolution of certain differential systems. These results are applied to nonlinear transport equations with prescribed exit values, Lagrangian intersections of convex-concave Hamiltonian systems, initial-value problems of dissipative systems, as well as evolution equations with periodic and anti-periodic solutions.
Keywords: Selfdual functionals, boundary value and initial-value problems..
Mathematics Subject Classification: Primary: 35F10, 35J65; Secondary: 47N10, 58E3.
Citation: Nassif Ghoussoub. Superposition of selfdual functionals in non-homogeneous boundary value problems and differential systems. Discrete & Continuous Dynamical Systems, 2008, 21 (1) : 187-220. doi: 10.3934/dcds.2008.21.187
[1]

Fei Guo, Bao-Feng Feng, Hongjun Gao, Yue Liu. On the initial-value problem to the Degasperis-Procesi equation with linear dispersion. Discrete & Continuous Dynamical Systems, 2010, 26 (4) : 1269-1290. doi: 10.3934/dcds.2010.26.1269
[2]

Sergei Avdonin, Fritz Gesztesy, Konstantin A. Makarov. Spectral estimation and inverse initial boundary value problems. Inverse Problems & Imaging, 2010, 4 (1) : 1-9. doi: 10.3934/ipi.2010.4.1
[3]

Aimin Huang, Roger Temam. The linear hyperbolic initial and boundary value problems in a domain with corners. Discrete & Continuous Dynamical Systems - B, 2014, 19 (6) : 1627-1665. doi: 10.3934/dcdsb.2014.19.1627
[4]

J. Colliander, A. D. Ionescu, C. E. Kenig, Gigliola Staffilani. Weighted low-regularity solutions of the KP-I initial-value problem. Discrete & Continuous Dynamical Systems, 2008, 20 (2) : 219-258. doi: 10.3934/dcds.2008.20.219
[5]

Vladimir V. Varlamov. On the initial boundary value problem for the damped Boussinesq equation. Discrete & Continuous Dynamical Systems, 1998, 4 (3) : 431-444. doi: 10.3934/dcds.1998.4.431
[6]

Colin J. Cotter, Darryl D. Holm. Geodesic boundary value problems with symmetry. Journal of Geometric Mechanics, 2010, 2 (1) : 51-68. doi: 10.3934/jgm.2010.2.51
[7]

Leo G. Rebholz, Dehua Wang, Zhian Wang, Camille Zerfas, Kun Zhao. Initial boundary value problems for a system of parabolic conservation laws arising from chemotaxis in multi-dimensions. Discrete & Continuous Dynamical Systems, 2019, 39 (7) : 3789-3838. doi: 10.3934/dcds.2019154
[8]

Elena Rossi. Well-posedness of general 1D initial boundary value problems for scalar balance laws. Discrete & Continuous Dynamical Systems, 2019, 39 (6) : 3577-3608. doi: 10.3934/dcds.2019147
[9]

V. A. Dougalis, D. E. Mitsotakis, J.-C. Saut. On initial-boundary value problems for a Boussinesq system of BBM-BBM type in a plane domain. Discrete & Continuous Dynamical Systems, 2009, 23 (4) : 1191-1204. doi: 10.3934/dcds.2009.23.1191
[10]

Shou-Fu Tian. Initial-boundary value problems for the coupled modified Korteweg-de Vries equation on the interval. Communications on Pure & Applied Analysis, 2018, 17 (3) : 923-957. doi: 10.3934/cpaa.2018046
[11]

Runzhang Xu, Mingyou Zhang, Shaohua Chen, Yanbing Yang, Jihong Shen. The initial-boundary value problems for a class of sixth order nonlinear wave equation. Discrete & Continuous Dynamical Systems, 2017, 37 (11) : 5631-5649. doi: 10.3934/dcds.2017244
[12]

Gilles Carbou, Bernard Hanouzet. Relaxation approximation of the Kerr model for the impedance initial-boundary value problem. Conference Publications, 2007, 2007 (Special) : 212-220. doi: 10.3934/proc.2007.2007.212
[13]

Changming Song, Hong Li, Jina Li. Initial boundary value problem for the singularly perturbed Boussinesq-type equation. Conference Publications, 2013, 2013 (special) : 709-717. doi: 10.3934/proc.2013.2013.709
[14]

Jun Zhou. Initial boundary value problem for a inhomogeneous pseudo-parabolic equation. Electronic Research Archive, 2020, 28 (1) : 67-90. doi: 10.3934/era.2020005
[15]

Hui Yang, Yuzhu Han. Initial boundary value problem for a strongly damped wave equation with a general nonlinearity. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021019
[16]

Shaoyong Lai, Yong Hong Wu, Xu Yang. The global solution of an initial boundary value problem for the damped Boussinesq equation. Communications on Pure & Applied Analysis, 2004, 3 (2) : 319-328. doi: 10.3934/cpaa.2004.3.319
[17]

Xianpeng Hu, Dehua Wang. The initial-boundary value problem for the compressible viscoelastic flows. Discrete & Continuous Dynamical Systems, 2015, 35 (3) : 917-934. doi: 10.3934/dcds.2015.35.917
[18]

Jong-Shenq Guo, Masahiko Shimojo. Blowing up at zero points of potential for an initial boundary value problem. Communications on Pure & Applied Analysis, 2011, 10 (1) : 161-177. doi: 10.3934/cpaa.2011.10.161
[19]

Zhiyuan Li, Xinchi Huang, Masahiro Yamamoto. Initial-boundary value problems for multi-term time-fractional diffusion equations with $ x $-dependent coefficients. Evolution Equations & Control Theory, 2020, 9 (1) : 153-179. doi: 10.3934/eect.2020001
[20]

Laurence Halpern, Jeffrey Rauch. Hyperbolic boundary value problems with trihedral corners. Discrete & Continuous Dynamical Systems, 2016, 36 (8) : 4403-4450. doi: 10.3934/dcds.2016.36.4403

2019 Impact Factor: 1.338

Tools

Metrics

  • PDF downloads (55)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences