5 problems

Euclidean and geodesic distance propagation conjecture. There exists such an obstacle $K$ and datum $(J,f)$ for which the limiting solution $u_\infty$ satisfies

Classification conjecture. All propagating solutions invading $\boldsymbol{0}$, except possibly semi-extinct monostable traveling waves, belong to

Consider the BGK-like kinetic equation … where $g(t,x,v)$ is the density, $v\in V$ is a velocity parameter, $M(v)$ is a reference velocity distribution, and $\rho_g$ is the integra…

Flattening conjecture. The only such $x$-monotone solutions are $x$-independent: they have the form

Let $u$ be the solution of the Cauchy problem considered in Theorem … xa(t)-xb(t)to+inftyquadtext{as }tto+infty. … , $x_a(t)-x_b(t)\to+\infty$ as $t\to+\infty$ for any $0<a<b<1$. T…