scholarly journals An inhomogeneous evolution equation involving the normalized infinity Laplacian with a transport term

2018 ◽  
Vol 17 (6) ◽  
pp. 2395-2421
Author(s):  
Fang Liu ◽  
Keyword(s):  
Evolution Equation ◽  
Infinity Laplacian ◽  
Transport Term

scholarly journals The infinity Laplacian with a transport term

2013 ◽  
Vol 398 (2) ◽  
pp. 752-765 ◽  
Author(s):  
Rafael López-Soriano ◽  
José C. Navarro-Climent ◽  
Julio D. Rossi
Keyword(s):  
Infinity Laplacian ◽  
Transport Term

Conserved Quantities for the General Linear Heat Equation

2016 ◽  
pp. 4437-4439
Author(s):  
Adil Jhangeer ◽  
Fahad Al-Mufadi
Keyword(s):  
Evolution Equation ◽  
Heat Equation ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Lagrangian Approach ◽  
General Linear ◽  
Conserved Quantities ◽  
Linear Heat ◽  
The Family ◽  
Partial Lagrangian

In this paper, conserved quantities are computed for a class of evolution equation by using the partial Noether approach [2]. The partial Lagrangian approach is applied to the considered equation, infinite many conservation laws are obtained depending on the coefficients of equation for each n. These results give potential systems for the family of considered equation, which are further helpful to compute the exact solutions.

scholarly journals Mass and spin for classical strings in dS3

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Klaas Parmentier
Keyword(s):  
Black Hole ◽  
Evolution Equation ◽  
Cosmic Strings ◽  
Center Of Mass ◽  
Open String ◽  
Conserved Quantities ◽  
Numerical Example ◽  
All Solutions

Abstract We demonstrate that all rigidly rotating strings with center of mass at the origin of the dS3 static patch satisfy the Higuchi bound. This extends the observation of Noumi et al. for the open GKP-like string to all solutions of the Larsen-Sanchez class. We argue that strings violating the bound end up expanding towards the horizon and provide a numerical example. Adding point masses to the open string only increases the mass/spin ratio. For segmented strings, we write the conserved quantities, invariant under Gubser’s algebraic evolution equation, in terms of discrete lightcone coordinates describing kink collisions. Randomly generated strings are found to have a tendency to escape through the horizon that is mostly determined by their energy. For rapidly rotating segmented strings with mass/spin < 1, the kink collisions eventually become causally disconnected. Finally we consider the scenario of cosmic strings captured by a black hole in dS and find that horizon friction can make the strings longer.

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