June  2010, 3(2): 339-349. doi: 10.3934/dcdss.2010.3.339

On a comprehensive class of linear material laws in classical mathematical physics

1. 

Institut für Analysis,Fachrichtung Mathematik, Technische Universität Dresden, D-01187 Dresden, Germany

Received  February 2009 Revised  August 2009 Published  April 2010

A class of evolutionary problems is considered, which covers a number of diverse initial boundary value problems of classical mathematical physics. The claim that this class is indeed to a large extent sufficiently general is exemplified by some specific models for visco-elastic solids.
Citation: Rainer Picard. On a comprehensive class of linear material laws in classical mathematical physics. Discrete & Continuous Dynamical Systems - S, 2010, 3 (2) : 339-349. doi: 10.3934/dcdss.2010.3.339
[1]

Tuan Anh Dao, Hironori Michihisa. Study of semi-linear $ \sigma $-evolution equations with frictional and visco-elastic damping. Communications on Pure & Applied Analysis, 2020, 19 (3) : 1581-1608. doi: 10.3934/cpaa.2020079

[2]

Khalid Addi, Oanh Chau, Daniel Goeleven. On some frictional contact problems with velocity condition for elastic and visco-elastic materials. Discrete & Continuous Dynamical Systems - A, 2011, 31 (4) : 1039-1051. doi: 10.3934/dcds.2011.31.1039

[3]

Grigory Panasenko, Ruxandra Stavre. Asymptotic analysis of a non-periodic flow in a thin channel with visco-elastic wall. Networks & Heterogeneous Media, 2008, 3 (3) : 651-673. doi: 10.3934/nhm.2008.3.651

[4]

Linglong Du. Long time behavior for the visco-elastic damped wave equation in $\mathbb{R}^n_+$ and the boundary effect. Networks & Heterogeneous Media, 2018, 13 (4) : 549-565. doi: 10.3934/nhm.2018025

[5]

Toyohiko Aiki. A free boundary problem for an elastic material. Conference Publications, 2007, 2007 (Special) : 10-17. doi: 10.3934/proc.2007.2007.10

[6]

Maria-Magdalena Boureanu, Andaluzia Matei, Mircea Sofonea. Analysis of a contact problem for electro-elastic-visco-plastic materials. Communications on Pure & Applied Analysis, 2012, 11 (3) : 1185-1203. doi: 10.3934/cpaa.2012.11.1185

[7]

H. Thomas Banks, Kidist Bekele-Maxwell, Lorena Bociu, Marcella Noorman, Giovanna Guidoboni. Local sensitivity via the complex-step derivative approximation for 1D Poro-Elastic and Poro-Visco-Elastic models. Mathematical Control & Related Fields, 2019, 9 (4) : 623-642. doi: 10.3934/mcrf.2019044

[8]

Irena Pawłow. Thermodynamically consistent Cahn-Hilliard and Allen-Cahn models in elastic solids. Discrete & Continuous Dynamical Systems - A, 2006, 15 (4) : 1169-1191. doi: 10.3934/dcds.2006.15.1169

[9]

Irena Pawłow, Wojciech M. Zajączkowski. Regular weak solutions to 3-D Cahn-Hilliard system in elastic solids. Conference Publications, 2007, 2007 (Special) : 824-833. doi: 10.3934/proc.2007.2007.824

[10]

Shui-Nee Chow, Kening Lu, Yun-Qiu Shen. Normal forms for quasiperiodic evolutionary equations. Discrete & Continuous Dynamical Systems - A, 1996, 2 (1) : 65-94. doi: 10.3934/dcds.1996.2.65

[11]

Alexander Mielke. Deriving amplitude equations via evolutionary $\Gamma$-convergence. Discrete & Continuous Dynamical Systems - A, 2015, 35 (6) : 2679-2700. doi: 10.3934/dcds.2015.35.2679

[12]

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

[13]

C. M. Khalique, G. S. Pai. Conservation laws and invariant solutions for soil water equations. Conference Publications, 2003, 2003 (Special) : 477-481. doi: 10.3934/proc.2003.2003.477

[14]

Boris Andreianov, Frédéric Lagoutière, Nicolas Seguin, Takéo Takahashi. Small solids in an inviscid fluid. Networks & Heterogeneous Media, 2010, 5 (3) : 385-404. doi: 10.3934/nhm.2010.5.385

[15]

James K. Knowles. On shock waves in solids. Discrete & Continuous Dynamical Systems - B, 2007, 7 (3) : 573-580. doi: 10.3934/dcdsb.2007.7.573

[16]

Francesco Maddalena, Danilo Percivale, Franco Tomarelli. Adhesive flexible material structures. Discrete & Continuous Dynamical Systems - B, 2012, 17 (2) : 553-574. doi: 10.3934/dcdsb.2012.17.553

[17]

Ying Hu, Shanjian Tang. Nonlinear backward stochastic evolutionary equations driven by a space-time white noise. Mathematical Control & Related Fields, 2018, 8 (3&4) : 739-751. doi: 10.3934/mcrf.2018032

[18]

Laura Caravenna, Annalisa Cesaroni, Hung Vinh Tran. Preface: Recent developments related to conservation laws and Hamilton-Jacobi equations. Discrete & Continuous Dynamical Systems - S, 2018, 11 (5) : ⅰ-ⅲ. doi: 10.3934/dcdss.201805i

[19]

Marianna Euler, Norbert Euler. Integrating factors and conservation laws for some Camassa-Holm type equations. Communications on Pure & Applied Analysis, 2012, 11 (4) : 1421-1430. doi: 10.3934/cpaa.2012.11.1421

[20]

Stephen Anco, Maria Rosa, Maria Luz Gandarias. Conservation laws and symmetries of time-dependent generalized KdV equations. Discrete & Continuous Dynamical Systems - S, 2018, 11 (4) : 607-615. doi: 10.3934/dcdss.2018035

2018 Impact Factor: 0.545

Metrics

  • PDF downloads (10)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]