In order to consider an energy super-critical semi-linear heat equation, Collot, Raphael, and Szeftel first revisit the construction of radially symmetric self-similar solutions performed through an ode approach (Troy, 1987 and Budd and Qi, 1989) and propose a bifurcation type argument (Biernat and Bizon, 2011) that allows for a sharp control of the spectrum of the corresponding linearized operator in suitable weighted spaces. Then they show how the sole knowledge of this spectral gap in weighted spaces implies the finite co-dimensional non-radial stability of these solutions for smooth well localized initial data using energy bounds. As a whole, they say, the scheme draws a route map for deriving the existence and stability of self-similar blow up in non-radial energy super-critical settings. Annotation ©2019 Ringgold, Inc., Portland, OR (protoview.com)
