6 problems

Consider the nonlinear heat equation studied in the paper and its initial-data space $\mathcal{H}_{a}$. The blowup pattern described in part $(i)$ of Theorem 1 is the finite-time,…

Minimal-mass classification conjecture. Up to the symmetries of the equation, the only non-scattering solutions are the soliton $e^{it}Q$ and its pseudoconformal transformation.

Classification of minimal-mass blowup solutions. Only the following two cases occur:

Rigidity conjecture. Any blowup solution must contain either the Jackiw–Pi vortex $Q$ or the pseudoconformal blowup solution $S$. The conjecture concerns the classification of blow…

Let $m$ be the order parameter in the higher-order semilinear parabolic equation denoted by. A nontrivial self-similar blowup solution is a self-similar blowup solution whose profi…

Let $U^*_{\alpha}$ be the final blowup profile associated with the constructed solution, and let $c^*$ be a positive constant. The profile itself satisfies a logarithmic asymptotic…