Nonlocal conservation laws with time delay

2019 ◽  
Vol 26 (6) ◽  
Author(s):  
Alexander Keimer ◽  
Lukas Pflug
Keyword(s):  
Time Delay ◽  
Conservation Laws ◽  
Nonlocal Conservation Laws

scholarly journals A convergent finite volume method for the Kuramoto equation and related nonlocal conservation laws

2018 ◽  
Vol 40 (1) ◽  
pp. 405-421 ◽  
Author(s):  
N Chatterjee ◽  
U S Fjordholm
Keyword(s):  
Initial Data ◽  
Conservation Laws ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Numerical Examples ◽  
Continuity Equations ◽  
Multiple Dimensions ◽  
Nonlocal Conservation Laws ◽  
Volume Method ◽  
Singular Data

Abstract We derive and study a Lax–Friedrichs-type finite volume method for a large class of nonlocal continuity equations in multiple dimensions. We prove that the method converges weakly to the measure-valued solution and converges strongly if the initial data is of bounded variation. Several numerical examples for the kinetic Kuramoto equation are provided, demonstrating that the method works well for both regular and singular data.

Potential Systems and Nonlocal Conservation Laws of Prandtl Boundary Layer Equations on the Surface of a Sphere

2017 ◽  
Vol 72 (4) ◽  
pp. 351-357 ◽  
Author(s):  
R. Naz
Keyword(s):  
Boundary Layer ◽  
Conservation Laws ◽  
Linear Combination ◽  
Conservation Law ◽  
Local Conservation ◽  
Boundary Layer Equations ◽  
Potential System ◽  
Nonlocal Conservation Laws ◽  
Prandtl Boundary Layer ◽  
Nonlocally Related Systems

Abstract:The potential systems and nonlocal conservation laws of Prandtl boundary layer equations on the surface of a sphere have been investigated. The multiplier approach yields two local conservation laws for the Prandtl boundary layer equations on the surface of a sphere. Two potential variables ψ and ϕ are introduced corresponding to first and second conservation law. Moreover, another potential variable p is introduced by considering the linear combination of both conservation laws. Two level one potential systems involving a single nonlocal variable ψ or ϕ are constructed. One level two potential system involving both nonlocal variables ψ and ϕ is established. The nonlocal variable p is utilised to derive a spectral potential system. The nonlocal conservation laws of Prandtl boundary layer equations on the surface of a sphere are derived by computing the local conservation laws of its potential systems. The nonlocal conservation laws are utilised to derive the further nonlocally related systems.

Conservation Laws and Soliton Solutions of the (1+1)-Dimensional Modified Improved Boussinesq Equation

2015 ◽  
Vol 70 (8) ◽  
pp. 669-672 ◽  
Author(s):  
Ozkan Guner ◽  
Sait San ◽  
Ahmet Bekir ◽  
Emrullah Yaşar
Keyword(s):  
Conservation Laws ◽  
Boussinesq Equation ◽  
Soliton Solutions ◽  
Ansatz Method ◽  
Nonlocal Conservation Laws ◽  
Dependent Model ◽  
Nonlinear Physical Phenomena ◽  
Physical Phenomena ◽  
Evolution Type ◽  
Partial Lagrangian

AbstractIn this work, we consider the (1+1)-dimensional modified improved Boussinesq (IMBq) equation. As the considered equation is of evolution type, no recourse to a Lagrangian formulation is made. However, we showed that by utilising the partial Lagrangian method and multiplier method, one can construct a number of local and nonlocal conservation laws for the IMBq equation. In addition, by using a solitary wave ansatz method, we obtained exact bright soliton solutions for this equation. The parameters of the soliton envelope (amplitude, widths, velocity) were obtained as function of the dependent model coefficients. Note that, it is always useful and desirable to construct exact solutions especially soliton-type envelope for the understanding of most nonlinear physical phenomena.

scholarly journals Control of a Time Delay System Arising From Linearized Conservation Laws

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 48524-48542 ◽  
Author(s):  
Daniela Danciu ◽  
Dan Popescu ◽  
Vladimir Rasvan
Keyword(s):  
Time Delay ◽  
Conservation Laws ◽  
Delay System ◽  
Time Delay System
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