6 problems

Let $\Omega\subset\mathbb{R}^N$, with $1\leq N\leq 3$, be a bounded domain with smooth boundary, and let $u_0\in H^2\cap H_0^1(\Omega)$. Let $\lambda^{*}$ be the critical parameter…

Let $\Omega\subset\mathbb{R}^N$, with $1\leq N\leq 3$, be a bounded domain with smooth boundary, and let $u_0\in H^2\cap H_0^1(\Omega)$. Consider equation (1.1), its solution…

Uniqueness conjecture. Entropy solutions of the equation in this more general setting should be unique.

The system under consideration describes interacting populations with population number $N$ and interaction coefficients $gamma_{ii}$. The analysis discussed here focuses on two po…

Conjecture on the sequence $(t_n)$. The sequence $(t_n)$ is strictly decreasing and satisfies

Mass-conservation conjecture. Conservation of mass should hold: for every solution with initial datum $u_0$, one has