1 Scalar reaction-diffusion equations - conditional symmetry, exact solutions and applications.- 2 Q-conditional symmetries of reaction-diffusion systems.- 3 Conditional symmetries and exact solutions of diffusive Lotka-Volterra systems.- 4 Q-conditional symmetries of the first type and exact solutions of nonlinear reaction-diffusion systems.- A List of reaction-diffusion systems and exact solutions.- Index.
Roman Cherniha graduated in mathematics from the Taras Shevchenko Kyiv State University (1981), and defended his PhD dissertation (1987) and habilitation (2003) at the Institute of Mathematics, NAS of Ukraine. During his early career, he gained substantial experience on the field of applied mathematics and physics at the Institute of Technical Heat Physics (Kyiv). Since 1992, he has held a permanent position at the Institute of Mathematics. He spent a few years abroad working at the Henri Poincare Unniversity (a temporary CNRS position) and the University of Nottingham (Marie Curie Research Fellow). He has a wide range of research interests including: non-linear partial differential equations (especially reaction-diffusion equations): Lie and conditional symmetries, exact solutions and their properties; development of new methods for analytically solving non-linear PDEs; application of modern methods for analytically solving nonlinear boundary-value problems arising in real world application; analytically and numerically solving boundary-value problems with free boundaries; development of mathematical models describing the specific processes arising in physics, biology and medicine.Vasyl' Davydovych graduated in mathematics from the Lesya Ukrainka Volyn National University (2009), and defended his PhD dissertation (2014) at the Institute of Mathematics, NAS of Ukraine. At present, he is a junior researcher at the Institute of Mathematics at the NAS of Ukraine. He is currently investigating nonlinear PDEs using symmetry-based methods. His primary aim is the study of nonlinear reaction-diffusion systems arising in real-world applications (such as the diffusive Lotka-Volterra type systems).
"The aim of this book is to identify particular solutions for a wide range of reaction-diffusion Systems ... . This book is primarily addressed to mathematicians working in the field of reaction-diffusion systems. Biological mathematicians can readily use the particular solutions that are listed in this book (rather convenient summary tables are given)." (Thomas Giletti, zbMATH 1391.35003, 2018)