We consider the nonlinear biharmonic Schr\"odinger equation $$i\partial_tu+(\Delta^2+\mu\Delta)u+f(u)=0,\qquad (\text{BNLS})$$ in critical Sobolev space $H^s(\R^N)$, where $N\ge1$, $\mu=0$ or $-1$, $0<s<\min\{\fc N2,8\}$ and $f(u)$ is a function that behaves like $\lambda\left|u\right|^{\alpha}u$ with $\lambda\in\mathbb{C},\alpha=\frac{8}{N-2s}$. prove existence uniqueness of global solutions t...

This paper is concerned with an inverse source problem for the stochastic biharmonic wave equation. The driven assumed to be a microlocally isotropic Gaussian random field its covariance operator being classical pseudo-differential operator. well-posedness of direct examined in distribution sense, and regularity solution discussed given rough source. For problem, strength source, involved princ...