Conformal conservation laws for second-order scalar fields

1976 ◽  
Vol 34 (2) ◽  
pp. 319-324 ◽  
Author(s):  
J. S. Blakeslee ◽  
J. D. Logan
Keyword(s):  
Conservation Laws ◽  
Scalar Fields ◽  
Second Order

scholarly journals Nonlinear conservation laws for the Schrödinger boundary value problems of second order

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ming Ren ◽  
Shiwei Yun ◽  
Zhenping Li
Keyword(s):  
Cauchy Problem ◽  
Conservation Laws ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Maximum Modulus ◽  
Second Order ◽  
Nonlinear Conservation Laws ◽  
The Cauchy Problem ◽  
Modulus Method ◽  
Semilinear Schrödinger Equation

AbstractIn this paper, we apply a reliable combination of maximum modulus method with respect to the Schrödinger operator and Phragmén–Lindelöf method to investigate nonlinear conservation laws for the Schrödinger boundary value problems of second order. As an application, we prove the global existence to the solution for the Cauchy problem of the semilinear Schrödinger equation. The results reveal that this method is effective and simple.

scholarly journals On a Theory for Analysing Second-Order Systems of Ordinary Discrete Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
J. J. H. Bashingwa ◽  
A. H. Kara
Keyword(s):  
Conservation Laws ◽  
Difference Equations ◽  
Second Order ◽  
Discrete Equations ◽  
Second Order Systems

We present geometric based methods for solving systems of discrete or difference equations and introduce a technique for finding conservation laws for such systems.

scholarly journals A novel second order accurate hybrid numerical approach for conservation laws

2008 ◽  
Vol 25 ◽  
pp. 91-113
Author(s):  
Pascal Jaisson ◽  
Florian De Vuyst
Keyword(s):  
Conservation Laws ◽  
Numerical Approach ◽  
Second Order

WENO-TVD schemes for hyperbolic conservation laws

Analysis ◽  
2007 ◽  
Vol 27 (1) ◽  
Author(s):  
Yousef Hashem Zahran
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Building Blocks ◽  
Second Order ◽  
Third Order ◽  
Weno Schemes ◽  
Hyperbolic Conservation ◽  
Systematic Assessment ◽  
The Third ◽  
Seventh Order

The purpose of this paper is twofold. Firstly we carry out a modification of the finite volume WENO (weighted essentially non-oscillatory) scheme of Titarev and Toro [14] and [15].This modification is done by using two fluxes as building blocks in spatially fifth order WENO schemes instead of the second order TVD flux proposed by Titarev and Toro [14] and [15]. These fluxes are the second order TVD flux [19] and the third order TVD flux [20].Secondly, we propose to use these fluxes as a building block in spatially seventh order WENO schemes. The numerical solution is advanced in time by the third order TVD Runge–Kutta method. A way to extend these schemes to general systems of nonlinear hyperbolic conservation laws, in one and two dimension is presented. Systematic assessment of the proposed schemes shows substantial gains in accuracy and better resolution of discontinuities, particularly for problems involving long time evolution containing both smooth and non-smooth features.

scholarly journals Second-order schemes for conservation laws with discontinuous flux modelling clarifier–thickener units

2010 ◽  
Vol 116 (4) ◽  
pp. 579-617 ◽  
Author(s):  
Raimund Bürger ◽  
Kenneth H. Karlsen ◽  
Héctor Torres ◽  
John D. Towers
Keyword(s):  
Conservation Laws ◽  
Second Order ◽  
Discontinuous Flux
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