Acta Appl Math (2013) 123:53–72 DOI 10.1007/s10440-012-9714-2 Radial Equivalence of Nonhomogeneous Nonlinear Diffusion Equations Razvan Gabriel Iagar · Guillermo Reyes · Ariel Sánchez Received: 7 September 2011 / Accepted: 2 April 2012 / Published online: 6 June 2012 © Springer Science+Business Media B.V. 2012 Abstract We establish one-to-one transformations and self-maps between nonlinear diffu- sion equations in nonhomogeneous media, where the density function is given by a power. We use these transformations to deduce new interesting self-similar, radially symmetric so- lutions of the equations. In particular, Barenblatt, dipole and focusing Aronson-Graveleau type solutions are deduced, and some equations with singular potentials are studied. The new solutions are example of interesting or unexpected mathematical features of these equations, providing also natural candidates for the asymptotic behavior. Keywords Non-homogeneous porous media · Self-similar solutions · Self-maps · Radially-symmetric solutions · Critical exponents · Non-homogeneous p-Laplacian equation Mathematics Subject Classification 35C06 · 35K10 · 35K55 · 35K65 R.G. Iagar ( ) Institute de Mathematiques de Toulouse, CNRS-UMR 5219, Route de Narbonne, 31062, Toulouse Cedex 9, France e-mail: razvan.iagar@imar.ro R.G. Iagar Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 014700, Bucharest, Romania G. Reyes Departamento de Matemática, E.T.S.I. de Caminos, Canales y Puertos, Universidad Politécnica de Madrid, 28040, Madrid, Spain A. Sánchez Departamento de Matemática Aplicada, Universidad Rey Juan Carlos, Móstoles, 28933, Madrid, Spain