6 problems

Let a nonlinear symmetric hyperbolic system in $n$ spatial dimensions have totally linearly degenerate structures. Suppose a smooth solution belongs to … with $s>\frac{n}{2}+1$. Ma…

Consider hyperbolic approximations of higher-order PDEs, with $q_0$ denoting the leading-order approximation to the original solution $u$ and $q_i$, $i\geq 1$, denoting the derivat…

The hyperbolic Monge–Ampère equation arises in the design of freeform optical surfaces that transfer a given light-source distribution to a desired target distribution. Compactness…

Let $w_\varepsilon$ be a minimizer of … subject to the boundary conditions $w(0,x)=w_0(x)$ and $w'(0,x)=w_1(x)$. For $p\geq2$, let … be the defocusing nonlinear wave equation, with…

Consider solutions of the full nonlinear Gowdy equations with an asymptotic expansion … where $k\geq 0$ and $\varphi$, $q$, and $\psi$ are prescribed. The quantity $k$ is the asymp…

Extension conjecture. The solution can be defined for $x\geq X_\infty$ as an entropy locally piecewise smooth solution outside the boundary, with infinite velocity on