7 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,…

Let $Q$ be the space-time domain, let $\vec{J}$ and $\vec{D}$ denote the tensorial variables, and let $\mathcal{\vec{G}}$ be an implicit constitutive function. Assume that…

Attainability conjecture.

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…

Uniqueness-without-large-solution conjecture. The implication

Minimal large-solution equality conjecture. The equality

Let $q>1$, and let $C_{2,q'}^{\mathbb R^N}$ denote the Bessel capacity associated with the conjugate exponent $q'$. Consider the necessary and sufficient conditions for the relevan…