On the stability of type I blow up for the energy super critical heat equation - Collot, Charles, 1990-; Raphaël, Pierre, 1975-; Szeftel, Jérémie, 1977- (Memoirs of the American Mathematical Society ;, 2019)
The authors consider the energy super critical semilinear heat equation \partial _{t}u=Δ u+u^{p}, x\in \mathbb{R}^3, p>5. The authors first revisit the construction of radially symmetric self similar solutions performed through an ode approach and propose a bifurcation type argument which allows for a sharp control of the spectrum of the corresponding linearized operator in suitable weighted spaces. They then show how the sole knowledge of this spectral gap in weighted spaces implies the finite codimensional nonradial stability of these solutions for smooth well localized initial data usi.