Nonlinear Reaction-Diffusion Systems : Conditional Symmetry, Exact Solutions and Their Applications in Biology

Chapters contain ideas for further theoretical generalizations and examples for real world applications

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 Poincaré 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).