We derive conditions on the initial data, including cases where the initial momentum density is not of one sign, that produce blow-up of the induced solution to the modified integrable Camassa-Holm equation with cubic nonlin-earity. The blow-up conditions are formulated in terms of the initial momentum density and the average initial energy.
The water level of Dongting Lake has changed because of the combined impact of climatic change and anthropogenic activities. A study of the long-term statistical properties of water level variations at Chenglingji station will help with the management of water resources in Dongting Lake. In this case, 54 years of water level data for Dongting Lake were… (More)
Reservoi r operation optimization (ROO) is a complicated dynamical ly constrained nonlinear problem that is important in the context of reservoir system operation. In this study, parallel deterministic dynamic programming (PDDP) and a hierarchic al adaptive genetic algorithm (HAGA) are proposed to solve the problem, which involves many conflicting… (More)
In this paper, we study a hydrodynamical system modeling the deformation of vesi-cle membrane in incompressible viscous fluids. In three dimensional case, we establish some uniqueness criteria of weak solutions for this system which reveal that the regularity of velocity field alone controls the uniqueness of weak solutions. A phase field approach in the… (More)
systems is to minimize the total operational cost subject to the system demand and reservoir requirements. In this paper we formulate the long-term scheduling problem of cascaded hydro energy systems with annual consumption and release constraints as a finite horizon Constrained Markov Decision Process (CMDP). We propose and develop a sensitivity-based… (More)