caa a22 4500 388108479 CHVBK 20180307125346.0 cr unu---uuuuu 161130s1999 xx s 000 0 eng 10.1017/S0308210500021429 doi S0308210500021429 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500021429 Stability analysis in order-preserving systems in the presence of symmetry [Elektronische Daten] Given an equation with a certain symmetry, such as symmetry with respect to rotation or translation, one of the most fundamental questions to ask is whether or not the symmetry of the equation is inherited by its solutions. We first discuss this question in a general framework of order-preserving dynamical systems under a group action and establish a theory concerning symmetry or monotonicity properties of stable equilibrium points. We then apply this general theory to nonlinear partial differential equations. Among other things, we prove the rotational symmetry of solutions for a class of nonlinear elliptic equations and the monotonicity of travelling waves of some nonlinear diffusion equations. We also discuss the stability of stationary or periodic solutions for equations of surface motion. Copyright © Royal Society of Edinburgh 1999 Ogiwara Toshiko Graduate School of Mathematical Sciences, University of Tokyo, Komaba, Tokyo 153, Japan Matano Hiroshi Graduate School of Mathematical Sciences, University of Tokyo, Komaba, Tokyo 153, Japan Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/2(1999), 395-438 0308-2105 129:2<395 1999 129 PRM https://doi.org/10.1017/S0308210500021429 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500021429 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ogiwara Toshiko Graduate School of Mathematical Sciences, University of Tokyo, Komaba, Tokyo 153, Japan NATIONALLICENCE 700 1- Matano Hiroshi Graduate School of Mathematical Sciences, University of Tokyo, Komaba, Tokyo 153, Japan NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/2(1999), 395-438 0308-2105 129:2<395 1999 129 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge