2011, 2011(Special): 737-746. doi: 10.3934/proc.2011.2011.737

Dynamic boundary conditions as limit of singularly perturbed parabolic problems

1. 

Grupo de Dinámica No Lineal. Universidad Pontificia Comillas de Madrid, C/Alberto Agulilera 23, 28015 Madrid, Spain

2. 

Departamento de Matemática Aplicada, Universidad Complutense de Madrid, Madrid 28040

Received  July 2010 Revised  March 2011 Published  October 2011

We obtain dynamic boundary conditions as a limit of parabolic problems with null flux where the time derivative concentrates near the boundary.
Citation: Ángela Jiménez-Casas, Aníbal Rodríguez-Bernal. Dynamic boundary conditions as limit of singularly perturbed parabolic problems. Conference Publications, 2011, 2011 (Special) : 737-746. doi: 10.3934/proc.2011.2011.737
[1]

Lahcen Maniar, Martin Meyries, Roland Schnaubelt. Null controllability for parabolic equations with dynamic boundary conditions. Evolution Equations and Control Theory, 2017, 6 (3) : 381-407. doi: 10.3934/eect.2017020

[2]

Raluca Clendenen, Gisèle Ruiz Goldstein, Jerome A. Goldstein. Degenerate flux for dynamic boundary conditions in parabolic and hyperbolic equations. Discrete and Continuous Dynamical Systems - S, 2016, 9 (3) : 651-660. doi: 10.3934/dcdss.2016019

[3]

Davide Guidetti. Classical solutions to quasilinear parabolic problems with dynamic boundary conditions. Discrete and Continuous Dynamical Systems - S, 2016, 9 (3) : 717-736. doi: 10.3934/dcdss.2016024

[4]

Abdelaziz Khoutaibi, Lahcen Maniar. Null controllability for a heat equation with dynamic boundary conditions and drift terms. Evolution Equations and Control Theory, 2020, 9 (2) : 535-559. doi: 10.3934/eect.2020023

[5]

Abdelaziz Khoutaibi, Lahcen Maniar, Omar Oukdach. Null controllability for semilinear heat equation with dynamic boundary conditions. Discrete and Continuous Dynamical Systems - S, 2022, 15 (6) : 1525-1546. doi: 10.3934/dcdss.2022087

[6]

Kuntal Bhandari, Franck Boyer. Boundary null-controllability of coupled parabolic systems with Robin conditions. Evolution Equations and Control Theory, 2021, 10 (1) : 61-102. doi: 10.3934/eect.2020052

[7]

Davide Guidetti. On hyperbolic mixed problems with dynamic and Wentzell boundary conditions. Discrete and Continuous Dynamical Systems - S, 2020, 13 (12) : 3461-3471. doi: 10.3934/dcdss.2020239

[8]

Idriss Boutaayamou, Lahcen Maniar, Omar Oukdach. Stackelberg-Nash null controllability of heat equation with general dynamic boundary conditions. Evolution Equations and Control Theory, 2021  doi: 10.3934/eect.2021044

[9]

Ángela Jiménez-Casas, Aníbal Rodríguez-Bernal. PDE problems with concentrating terms near the boundary. Communications on Pure and Applied Analysis, 2020, 19 (4) : 2147-2195. doi: 10.3934/cpaa.2020095

[10]

Alexandre Nolasco de Carvalho, Marcos Roberto Teixeira Primo. Spatial homogeneity in parabolic problems with nonlinear boundary conditions. Communications on Pure and Applied Analysis, 2004, 3 (4) : 637-651. doi: 10.3934/cpaa.2004.3.637

[11]

Ciprian G. Gal, Mahamadi Warma. Elliptic and parabolic equations with fractional diffusion and dynamic boundary conditions. Evolution Equations and Control Theory, 2016, 5 (1) : 61-103. doi: 10.3934/eect.2016.5.61

[12]

Davide Guidetti. Parabolic problems with general Wentzell boundary conditions and diffusion on the boundary. Communications on Pure and Applied Analysis, 2016, 15 (4) : 1401-1417. doi: 10.3934/cpaa.2016.15.1401

[13]

Ángela Jiménez-Casas, Aníbal Rodríguez-Bernal. Boundary feedback as a singular limit of damped hyperbolic problems with terms concentrating at the boundary. Discrete and Continuous Dynamical Systems, 2019, 39 (9) : 5125-5147. doi: 10.3934/dcds.2019208

[14]

Carmen Calvo-Jurado, Juan Casado-Díaz, Manuel Luna-Laynez. Parabolic problems with varying operators and Dirichlet and Neumann boundary conditions on varying sets. Conference Publications, 2007, 2007 (Special) : 181-190. doi: 10.3934/proc.2007.2007.181

[15]

El Mustapha Ait Ben Hassi, Salah-Eddine Chorfi, Lahcen Maniar, Omar Oukdach. Lipschitz stability for an inverse source problem in anisotropic parabolic equations with dynamic boundary conditions. Evolution Equations and Control Theory, 2021, 10 (4) : 837-859. doi: 10.3934/eect.2020094

[16]

Nicola Abatangelo, Sven Jarohs, Alberto Saldaña. Positive powers of the Laplacian: From hypersingular integrals to boundary value problems. Communications on Pure and Applied Analysis, 2018, 17 (3) : 899-922. doi: 10.3934/cpaa.2018045

[17]

De-Han Chen, Daijun Jiang, Irwin Yousept, Jun Zou. Addendum to: "Variational source conditions for inverse Robin and flux problems by partial measurements". Inverse Problems and Imaging, 2022, 16 (2) : 481-481. doi: 10.3934/ipi.2022003

[18]

De-Han Chen, Daijun Jiang, Irwin Yousept, Jun Zou. Variational source conditions for inverse Robin and flux problems by partial measurements. Inverse Problems and Imaging, 2022, 16 (2) : 283-304. doi: 10.3934/ipi.2021050

[19]

Chunlai Mu, Zhaoyin Xiang. Blowup behaviors for degenerate parabolic equations coupled via nonlinear boundary flux. Communications on Pure and Applied Analysis, 2007, 6 (2) : 487-503. doi: 10.3934/cpaa.2007.6.487

[20]

Roland Schnaubelt. Center manifolds and attractivity for quasilinear parabolic problems with fully nonlinear dynamical boundary conditions. Discrete and Continuous Dynamical Systems, 2015, 35 (3) : 1193-1230. doi: 10.3934/dcds.2015.35.1193

 Impact Factor: 

Metrics

  • PDF downloads (79)
  • HTML views (0)
  • Cited by (0)

[Back to Top]