6 problems

Consider the laminated beam system with dynamic Venttsel-type boundary conditions and its linear operator defined in the paper. Boundary-control reduction conjecture. By applying C…

Let $h>0$ and let $u\in\ell^2((h\mathbb{Z})^n)$ solve the stationary discrete Schrödinger equation … under the finiteness assumptions on $\|q\|_\infty$ and $\|u\|_2$ appearing in t…

Let $\Omega$ be the spatial domain in the mean field games system, and suppose that Lemmata 2.1 and 2.2 are established when $\Omega$ is a rectangular prism. Domain-extension conje…

Let $\Omega\subset\mathbb{R}^n$ be a bounded domain, and consider the fourth-order nonlinear Schrödinger equation with insensitizing controls in the $N$-dimensional setting. The Ca…

Let $u$ solve the half-order time-fractional diffusion equation with source $g(x,t)=f(x)R(x,t)$ in $Q$, under the zero initial condition and homogeneous Dirichlet boundary conditio…

Let $u$ be the solution and let $E_2u$ denote the energy appearing in Proposition B.asymp. Let $\kappa$ be the parameter in the weighted boundary quantity, and let an appropriate f…