A special self-similar solution and existence of global solutions for a reaction-diffusion equation with Hardy potential

Existence and uniqueness of a specific self-similar solution is established for the following reaction-diffusion equation with Hardy singular potential?tu=?um+|x|?2up,(x,t)?RN×(0,?), in range exponents 1?p0 p?[1,?). As an application this solution, shown that there exists least to Cauchy problem associated previous bounded, nonnegative compactly supported initial condition u0, contrasting results literature critical limit p=m.