4 problems

Let $d$ denote the spatial dimension, and consider quasilinear Klein–Gordon equations with smooth, small initial data, without assuming that the data are localized. The lifespan is…

Let $\mathcal{U}_{T}$ be the state space of admissible pairs $U$, let $X$ and $X_{2\beta}$ be the spaces used for the stochastic evolution equation, let $H$ be a separable Hilbert…

Let a quasilinear SPDE have noise coefficient $\sigma$, and suppose that the corresponding deterministic PDE is obtained by setting $\sigma\equiv 0$. Global-existence noise conject…

Nonexistence conjecture. There are quasilinear wave equations of the form $$ for which there exists initial data such that there does not exist any UGHD.