Symmetries and solutions for a Fisher equation with a proliferation term involving tumor development

Abstract

We consider a generalized Fisher equation involving tumor development from the point of view of the theory of symmetry reductions in partial differential equations. The study of this equation is relevant as it includes generalizations within the proliferation rate, being interpreted in terms of the total mass of the tumor. Classical Lie point symmetries admitted by the equation are determined. Finally, we obtain some biologically meaningful solutions in terms of a hyperbolic tangent function, which describes the tumor dynamics.