4 problems

Let $u$ be a nonnegative weak dual solution of the porous medium-type evolution problem on a bounded domain $\mega$, with first eigenfunction $\hi_1$ of the underlying operator and…

Let $u$ solve the relativistic porous medium equation … A discontinuity is said to form when the solution develops a jump discontinuity, and the support expands when the spatial su…

Let $\gamma(t)=\frac{1}{N}\sum_{i=1}^N\delta_{X_i(t)}$ be the empirical measure of a rank-based particle system, and let $w$ denote the cumulative distribution function in the limi…

Changing-index conjecture. The value $\varepsilon=0$ is a point of changing index for the family $\{F_l\}$, and the result corresponding to Krasnosel'skii's Theorem 56.2 applies to…