CONTINUOUS SOLUTION FOR A NON-LINEAR EIKONAL SYSTEM

被引：1
作者：
El Hajj, Ahmad [1 ]
Oussaily, Aya [1 ]
机构：
[1] Univ Technol Compiegne, LMAC, F-60205 Compiegne, France
来源：
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2021年 / 20卷 / 11期
关键词：
Hamilton-Jacobi system; non-linear eikonal system; non-linear hyper-bolic system; entropy estimates; viscosity solution; DIAGONAL HYPERBOLIC SYSTEMS; VISCOSITY SOLUTIONS; GLOBAL EXISTENCE; EQUATIONS; DYNAMICS;
D O I：
10.3934/cpaa.2021131
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this work, we are dealing with a non-linear eikonal system in one dimensional space that describes the evolution of interfaces moving with non-signed strongly coupled velocities. We prove a global existence result in the framework of continuous viscosity solution. The approach is made by adding a viscosity term and passing to the limit for vanishing viscosity, relying on a new gradient entropy and BV estimates. A uniqueness result is also proved through a comparison principle property.
引用
收藏
页码：3779 / 3807
页数：29
相关论文
共 20 条
[1]  
Adams R.A., 2003, Sobolev spaces
[2]  
Bardi M., 1997, OPTIMAL CONTROL VISC
[3]  
Barles G., 1994, MATH APPL, V17
[4]   Vanishing viscosity solutions of nonlinear hyperbolic systems [J].
Bianchini, S ;
Bressan, A .
ANNALS OF MATHEMATICS, 2005, 161 (01) :223-342
[5]   Global existence results for eikonal equation with BV initial data [J].
Boudjerada, R. ;
El Hajj, A. .
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2015, 22 (04) :947-978
[6]   Global Existence for a System of Non-Linear and Non-Local Transport Equations Describing the Dynamics of Dislocation Densities [J].
Cannone, Marco ;
El Hajj, Ahmad ;
Monneau, Regis ;
Ribaud, Francis .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2010, 196 (01) :71-96
[7]   USERS GUIDE TO VISCOSITY SOLUTIONS OF 2ND-ORDER PARTIAL-DIFFERENTIAL EQUATIONS [J].
CRANDALL, MG ;
ISHII, H ;
LIONS, PL .
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 27 (01) :1-67
[8]  
El Hajj A, 2008, MATH COMPUT, V77, P789, DOI 10.1090/S0025-5718-07-02038-8
[9]   Well-posedness theory for a nonconservative burgers-type system arising in dislocation dynamics [J].
El Hajj, Ahmad .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2007, 39 (03) :965-986
[10]   BV SOLUTION FOR A NON-LINEAR HAMILTON-JACOBI SYSTEM [J].
El Hajj, Ahmad ;
Ibrahim, Hassan ;
Rizik, Vivian .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2021, 41 (07) :3273-3293
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