scholarly journals A scalable exponential-DG approach for nonlinear conservation laws: With application to Burger and Euler equations

2021 ◽  
Vol 385 ◽  
pp. 114031
Author(s):  
Shinhoo Kang ◽  
Tan Bui-Thanh
Keyword(s):  
Conservation Laws ◽  
Euler Equations ◽  
Nonlinear Conservation Laws

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.

Lagrangian Mechanics

2019 ◽  
pp. 53-82
Author(s):  
David D. Nolte
Keyword(s):  
Dynamical Systems ◽  
Conservation Laws ◽  
Euler Equations ◽  
Virial Theorem ◽  
Variational Calculus ◽  
Mechanical Action ◽  
Lagrange Equations ◽  
Time Average ◽  
The Difference ◽  
Kinetic And Potential Energies

Dynamical systems follow trajectories for which the mechanical action integrated along the trajectory is an extremum. The action is defined as the time average of the difference between kinetic and potential energies, which is also the time average of the Lagrangian. Once a Lagrangian has been defined for a system, the Euler equations of variational calculus lead to the Euler–Lagrange equations of dynamics. This chapter explores applications of Lagrangians and the use of Lagrange’s undetermined multipliers. Conservation laws, central forces, and the virial theorem are developed and explained.

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