Sensor deployment for pipeline leakage detection via optimal boundary control strategies
Chao Xu Yimeng Dong Zhigang Ren Huachen Jiang Xin Yu
Journal of Industrial & Management Optimization 2015, 11(1): 199-216 doi: 10.3934/jimo.2015.11.199
We consider a multi-agent control problem using PDE techniques for a novel sensing problem arising in the leakage detection and localization of offshore pipelines. A continuous protocol is proposed using parabolic PDEs and then a boundary control law is designed using the maximum principle. Both analytical and numerical solutions of the optimality conditions are studied.
keywords: Offshore pipeline network leakage detection optimal control. continuation approach multi-agent system partial differential equations Lagrangian sensor
Generalized and weighted Strichartz estimates
Jin-Cheng Jiang Chengbo Wang Xin Yu
Communications on Pure & Applied Analysis 2012, 11(5): 1723-1752 doi: 10.3934/cpaa.2012.11.1723
In this paper, we explore the relations between different kinds of Strichartz estimates and give new estimates in Euclidean space $\mathbb{R}^n$. In particular, we prove the generalized and weighted Strichartz estimates for a large class of dispersive operators including the Schrödinger and wave equation. As a sample application of these new estimates, we are able to prove the Strauss conjecture with low regularity for dimension $2$ and $3$.
keywords: Generalized Strichartz estimates weighted Strichartz estimates Strauss conjecture semilinear wave equations. angular regularity

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