Plenary Lecture

Symmetry Analysis, Conservation Laws and Exact Solutions for a Generalized Diffusion Equation

Professor Maria Luz Gandarias
Department of Mathematics
Faculty of Science
University of Cádiz, Spain

Abstract: Population dynamics models, bacterial growth problems as well as development and engineering problems are usually modelled by diffusion reaction equations. In this talk, we consider a generalized reaction-diffusion 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 we get analitical exact solutions and we study their behavior for some particular cases of the equation, that present several applications in the mathematical biological and engineering field 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 current research interests include group analysis, methods of group transformation: classical symmetries, nonclassical methods , direct methods and conservation laws applied to ordinary differential equations and partial 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.

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