Transformations of Self-Similar Solutions for porous medium equations of fractional type
Diana Stan, Félix del Teso, Vázquez, Juan Luis · arXiv (Cornell University) · 2014
We consider four different models of nonlinear diffusion equations involving fractional Laplacians and study the existence and properties of classes of self-similar solutions. Such solutions are an important tool in developing the general theory. We introduce a number of transformations that allow us to map complete classes of solutions of one equation into those of another one, thus providing us with a number of new solutions, as well as interesting connections. Special attention is paid to the property of finite propagation.