3 problems

Let $u(x,t)$ solve the Neumann problem … with … and initial data $u(x,0)=u_0(x)$, where $u_0(x)>0$ for some $x$. Long-time convergence conjecture. … The claim describes the predict…

Let $p_{\mathbb{U}}(t,x,y)$ denote the heat kernel for the Laplacian with Neumann boundary conditions on the unit ball … in $\mathbb{R}^{n}$, where $n\in\mathbb{N}^{\ast}$. The fun…

Let $\Omega$ be a bounded convex domain in the plane symmetric with respect to the $x$-axis, and let $p^N_{\Omega}(t,z,w)$ be its Neumann heat kernel. Let $f:\mathbb{B}\to\Omega$ b…