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 & Continuous Dynamical Systems - A, 2006, 14 (1) : i-iii. doi: 10.3934/dcds.2006.14.1i
[1]

Eduard Feireisl, Mirko Rokyta, Josef Málek. Preface. Discrete & Continuous Dynamical Systems - S, 2008, 1 (3) : i-iii. doi: 10.3934/dcdss.2008.1.3i
[2]

Christian Kanzow, Dong-Hui Li, Nobuo Yamashita. Preface. Numerical Algebra, Control & Optimization, 2011, 1 (1) : i-v. doi: 10.3934/naco.2011.1.1i
[3]

Zhaosheng Feng, Wei Feng. Preface. Discrete & Continuous Dynamical Systems - S, 2014, 7 (6) : i-i. doi: 10.3934/dcdss.2014.7.6i
[4]

Cheng-Chew Lim, Song Wang. Preface. Journal of Industrial & Management Optimization, 2008, 4 (1) : i-ii. doi: 10.3934/jimo.2008.4.1i
[5]

Eduard Feireisl, Josef Málek, Mirko Rokyta. Preface. Discrete & Continuous Dynamical Systems - S, 2010, 3 (3) : i-ii. doi: 10.3934/dcdss.2010.3.3i
[6]

Vadim Kaloshin, Sergey Lototsky, Michael Röckner. Preface. Discrete & Continuous Dynamical Systems - B, 2006, 6 (4) : i-ii. doi: 10.3934/dcdsb.2006.6.4i
[7]

Thorsten Koch, Xiaoling Sun. Preface. Numerical Algebra, Control & Optimization, 2012, 2 (4) : i-ii. doi: 10.3934/naco.2012.2.4i
[8]

Urszula Ledzewicz, Marek Galewski, Andrzej Nowakowski, Andrzej Swierniak, Agnieszka Kalamajska, Ewa Schmeidel. Preface. Discrete & 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 & Continuous Dynamical Systems - S, 2018, 11 (4) : i-ii. doi: 10.3934/dcdss.201804i
[10]

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

Shengji Li, Nan-Jing Huang, Xinmin Yang. Preface. Numerical Algebra, Control & Optimization, 2011, 1 (3) : i-ii. doi: 10.3934/naco.2011.1.3i
[12]

Iván Area, Alberto Cabada, José Ángel Cid, Daniel Franco, Eduardo Liz, Rosana Rodríguez-López. Preface. Discrete & Continuous Dynamical Systems - B, 2020, 25 (2) : ⅰ-ⅳ. doi: 10.3934/dcdsb.2019269
[13]

Carlos Castillo-Chavez, Gerardo Chowell. Preface. Mathematical Biosciences & Engineering, 2011, 8 (1) : i-vi. doi: 10.3934/mbe.2011.8.1i
[14]

P. De Maesschalck, Freddy Dumortier, Martin Wechselberger. Preface. Discrete & Continuous Dynamical Systems - S, 2009, 2 (4) : i-iii. doi: 10.3934/dcdss.2009.2.4i
[15]

Wei Kang, Liang Ke, Qi Wang. Preface. Discrete & Continuous Dynamical Systems - B, 2007, 8 (3) : i-i. doi: 10.3934/dcdsb.2007.8.3i
[16]

Noureddine Alaa, Marc Dambrine, Antoine Henrot, Alain Miranville. Preface. Communications on Pure & Applied Analysis, 2012, 11 (6) : i-ii. doi: 10.3934/cpaa.2012.11.6i
[17]

Ricardo Carretero-González, Jesús Cuevas Maraver, Dimitri J. Frantzeskakis, P.G. Kevrekidis, Faustino Palmero Acebedo. Preface. Discrete & Continuous Dynamical Systems - S, 2011, 4 (5) : i-iii. doi: 10.3934/dcdss.2011.4.5i
[18]

Zhaosheng Feng, Jinzhi Lei. Preface. Discrete & Continuous Dynamical Systems - B, 2011, 16 (2) : i-iv. doi: 10.3934/dcdsb.2011.16.2i
[19]

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
[20]

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

2019 Impact Factor: 1.338

Tools

Metrics

  • PDF downloads (18)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences