Nonlinear evolution equations with exponential nonlinearities: conditional symmetries and exact solutions
Volume 93 / 2011
Banach Center Publications 93 (2011), 105-115
MSC: Primary 35Q92;
Secondary 22E70
DOI: 10.4064/bc93-0-9
Abstract
New $Q$-conditional symmetries for a class of reaction-diffusion-convection equations with exponential diffusivities are derived. It is shown that the known results for reaction-diffusion equations with exponential diffusivities follow as particular cases from those obtained here but not vice versa. The symmetries obtained are applied to construct exact solutions of the relevant nonlinear equations. An application of exact solutions to solving a boundary-value problem with constant Dirichlet conditions is presented.
