Plenary Lecture
Symmetry Analysis, Conservation Laws and Exact Solutions for a Generalized Fisher Equation
Professor Maria Luz Gandarias
Faculty of Science
University of Cadiz
Spain
E-mail: marialuz.gandarias@uca.es
Abstract: Fishers equation is commonly used in biology for population dynamics models and in bacterial growth problems as well as development and growth of solid tumours. Generalizations of the Fisher equation are needed to more accutarely model complex diffusion and reactions effects found in many biological systems. In this talk, we consider a generalized reaction-diffusion Fisher equation by the point of view of Lie symmetry analysis. A classification of all the low-order conservation laws is obtained. The optimal system is discussed and all the reductions are derived from the optimal system of subalgebras. Some of the reduced equations admit Lie symmetries which yield to further reductions Moreover, we find analytical solutions of an interface problem for special cases of diffusion and proliferation.
Brief Biography of the Speaker: Maria Luz Gandarias received her PhD degree (Mathematics) from the University of Sevilla Spain. She joined the University of Cádiz in 1974. Presently she is a full professor in the Department of Mathematical of the University of Cádiz, she has supervised 4 PhD and 2 Masters students to date. Hers research interests are in the applications of Lie group methods to differential equations. She has published more than 110 research articles with more tan 500 citations, in various international peer-reviewed journals with high impact factors and has delivered research talks at many international conferences. She is on the Editorial boards of some international journals and has reviewed research papers for more than 20 academic journals.