On existence and uniqueness of the global weak solution for a shallow water equation

2012 ◽  
Vol 218 (23) ◽  
pp. 11410-11420 ◽  
Author(s):  
Yunxi Guo ◽  
Shaoyong Lai ◽  
Yonghong Wu
Keyword(s):  
Weak Solution ◽  
Shallow Water ◽  
Existence And Uniqueness ◽  
Shallow Water Equation ◽  
Global Weak Solution

The global weak solution for the shallow water wave model of moderate amplitude

2016 ◽  
Vol 96 (4) ◽  
pp. 663-678
Author(s):  
Yunxi Guo ◽  
Yonghong Wu ◽  
Shaoyong Lai ◽  
Lou Caccetta
Keyword(s):  
Weak Solution ◽  
Shallow Water ◽  
Water Wave ◽  
Wave Model ◽  
Global Weak Solution ◽  
Shallow Water Wave

scholarly journals On the 2D Ericksen–Leslie equations with anisotropic energy and external forces

2021 ◽  
Author(s):  
Zdzislaw Brzeźniak ◽  
Gabriel Deugoué ◽  
Paul André Razafimandimby
Keyword(s):  
Weak Solution ◽  
Initial Data ◽  
Existence And Uniqueness ◽  
Global Weak Solution ◽  
Energy Modeling ◽  
External Control ◽  
Global Weak Solutions ◽  
External Data ◽  
Anisotropic Energy ◽  
External Forces

AbstractIn this paper we consider the 2D Ericksen–Leslie equations which describe the hydrodynamics of nematic liquid crystal with external body forces and anisotropic energy modeling the energy of applied external control such as magnetic or electric field. Under general assumptions on the initial data, the external data and the anisotropic energy, we prove the existence and uniqueness of global weak solutions with finitely many singular times. If the initial data and the external forces are sufficiently small, then we establish that the global weak solution does not have any singular times and is regular as long as the data are regular.

scholarly journals Optimal control of a viscous generalized θ-type dispersive equation with weak dissipation

2020 ◽  
Vol 18 (1) ◽  
pp. 1302-1316
Author(s):  
Guobing Fan ◽  
Zhifeng Yang
Keyword(s):  
Boundary Condition ◽  
Optimal Control ◽  
Weak Solution ◽  
Existence And Uniqueness ◽  
Optimal Solution ◽  
Dispersive Equation ◽  
Weak Dissipation ◽  
Formula Type

Abstract In this paper, we investigate the problem for optimal control of a viscous generalized \theta -type dispersive equation (VG \theta -type DE) with weak dissipation. First, we prove the existence and uniqueness of weak solution to the equation. Then, we present the optimal control of a VG \theta -type DE with weak dissipation under boundary condition and prove the existence of optimal solution to the problem.

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