Stable blowup profile for a semilinear heat equation with spatially inhomogeneous nonlinearity

We study the focusing semilinear heat equation with an additional defocusing Hénon-type nonlinearity, the coupling of which is measured by a constant $c >0$. For c ∈ (0,c^*), the model admits a closed-form self-similar blowup solution in every space dimension d ≥ 1. Restricting ourselves to the three-dimensional case, we study the stability of this solution under small non-radial perturbations. By working in intersection Sobolev spaces with additional angular regularity, we prove finite co-dimension stability for all admissible values of c. Furthermore, we analyze the spectrum of the underlying linearized operator and we prove stable blowup for the cubic-quintic case and c sufficiently close to c^*. Finally, we discuss the situation for small values of c and use a modified version of the classical GGMT criterion to give an upper bound on the number of unstable eigenvalues.