American Institute of Mathematical Sciences

Advanced
January  2006, 14(1): i-iii. doi: 10.3934/dcds.2006.14.1i

Preface

Peter Poláčik 1, and  Eiji Yanagida 2,

1. 

School of Mathematics, University of Minnesota, Minneapolis, MN 55455
2. 

Mathematical Institute Tohoku University, 6-3Aoba, Aramaki, Aoba-ku, Sendai-shi, 980-8578

Published  October 2005

Interaction between nonlinearity and diffusion is a fascinating subject. Many interesting phenomena are known to result from such interaction, for example, generation of interfaces and singularities, formation of spatial and temporal patterns, propagation of waves, symmetrization and symmetry-breaking of solutions, and so on. Nonlinear diffusive systems have undergone a thorough investigation aimed at mathematical understanding of the mechanisms behind the phenomena.
The analysis serving this aim uses various classical and newly developed techniques relying on results from the bifurcation theory, singular perturbation theory, variational method, and the theory of finite and infinite dimensional dynamical systems. The qualitative theory of parabolic and elliptic equations has been developing extensively in the last few decades, and a lot of important, interesting and beautiful results have been obtained concerning the dynamics of solutions and qualitative description of steady states.

For more information please click the “Full Text” above.
Citation: Peter Poláčik, Eiji Yanagida. Preface. Discrete and Continuous Dynamical Systems, 2006, 14 (1) : i-iii. doi: 10.3934/dcds.2006.14.1i
[1]

Christian Kanzow, Dong-Hui Li, Nobuo Yamashita. Preface. Numerical Algebra, Control and Optimization, 2011, 1 (1) : i-v. doi: 10.3934/naco.2011.1.1i
[2]

Thorsten Koch, Xiaoling Sun. Preface. Numerical Algebra, Control and Optimization, 2012, 2 (4) : i-ii. doi: 10.3934/naco.2012.2.4i
[3]

Eduard Feireisl, Josef Málek, Mirko Rokyta. Preface. Discrete and Continuous Dynamical Systems - S, 2010, 3 (3) : i-ii. doi: 10.3934/dcdss.2010.3.3i
[4]

Eduard Feireisl, Mirko Rokyta, Josef Málek. Preface. Discrete and Continuous Dynamical Systems - S, 2008, 1 (3) : i-iii. doi: 10.3934/dcdss.2008.1.3i
[5]

Iván Area, Alberto Cabada, José Ángel Cid, Daniel Franco, Eduardo Liz, Rosana Rodríguez-López. Preface. Discrete and Continuous Dynamical Systems - B, 2020, 25 (2) : i-iv. doi: 10.3934/dcdsb.2019269
[6]

Carlos Castillo-Chavez, Gerardo Chowell. Preface. Mathematical Biosciences & Engineering, 2011, 8 (1) : i-vi. doi: 10.3934/mbe.2011.8.1i
[7]

P. De Maesschalck, Freddy Dumortier, Martin Wechselberger. Preface. Discrete and Continuous Dynamical Systems - S, 2009, 2 (4) : i-iii. doi: 10.3934/dcdss.2009.2.4i
[8]

Urszula Ledzewicz, Marek Galewski, Andrzej Nowakowski, Andrzej Swierniak, Agnieszka Kalamajska, Ewa Schmeidel. Preface. Discrete and Continuous Dynamical Systems - B, 2014, 19 (8) : i-ii. doi: 10.3934/dcdsb.2014.19.8i
[9]

Chaudry Masood Khalique, Maria Luz Gandarais, Mufid Abudiab. Preface. Discrete and Continuous Dynamical Systems - S, 2018, 11 (4) : i-ii. doi: 10.3934/dcdss.201804i
[10]

Zhouping Xin, Tong Yang. Preface. Discrete and Continuous Dynamical Systems - S, 2016, 9 (6) : i-ii. doi: 10.3934/dcdss.201606i
[11]

Zhaosheng Feng, Wei Feng. Preface. Discrete and Continuous Dynamical Systems - S, 2014, 7 (6) : i-i. doi: 10.3934/dcdss.2014.7.6i
[12]

Cheng-Chew Lim, Song Wang. Preface. Journal of Industrial and Management Optimization, 2008, 4 (1) : i-ii. doi: 10.3934/jimo.2008.4.1i
[13]

Vadim Kaloshin, Sergey Lototsky, Michael Röckner. Preface. Discrete and Continuous Dynamical Systems - B, 2006, 6 (4) : i-ii. doi: 10.3934/dcdsb.2006.6.4i
[14]

Wei Kang, Liang Ke, Qi Wang. Preface. Discrete and Continuous Dynamical Systems - B, 2007, 8 (3) : i-i. doi: 10.3934/dcdsb.2007.8.3i
[15]

Noureddine Alaa, Marc Dambrine, Antoine Henrot, Alain Miranville. Preface. Communications on Pure and Applied Analysis, 2012, 11 (6) : i-ii. doi: 10.3934/cpaa.2012.11.6i
[16]

Shengji Li, Nan-Jing Huang, Xinmin Yang. Preface. Numerical Algebra, Control and Optimization, 2011, 1 (3) : i-ii. doi: 10.3934/naco.2011.1.3i
[17]

Avner Friedman, Mirosław Lachowicz, Urszula Ledzewicz, Monika Joanna Piotrowska, Zuzanna Szymanska. Preface. Mathematical Biosciences & Engineering, 2017, 14 (1) : i-i. doi: 10.3934/mbe.201701i
[18]

Baojun Bian, Shanjian Tang, Qi Zhang. Preface. Discrete and Continuous Dynamical Systems, 2015, 35 (11) : i-iv. doi: 10.3934/dcds.2015.35.11i
[19]

Zhaosheng Feng, Jinzhi Lei. Preface. Discrete and Continuous Dynamical Systems - B, 2011, 16 (2) : i-iv. doi: 10.3934/dcdsb.2011.16.2i
[20]

Frédéric Coquel, Edwige Godlewski, Jean-Marc Hérard, Jacques Segré. Preface. Networks and Heterogeneous Media, 2010, 5 (3) : i-ii. doi: 10.3934/nhm.2010.5.3i

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (24)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy