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On positive solutions of the elliptic sine-Gordon equation
On homogenization of nonlinear hyperbolic equations
1. | Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, United States |
[1] |
Mogtaba Mohammed, Mamadou Sango. Homogenization of nonlinear hyperbolic stochastic partial differential equations with nonlinear damping and forcing. Networks and Heterogeneous Media, 2019, 14 (2) : 341-369. doi: 10.3934/nhm.2019014 |
[2] |
Liselott Flodén, Jens Persson. Homogenization of nonlinear dissipative hyperbolic problems exhibiting arbitrarily many spatial and temporal scales. Networks and Heterogeneous Media, 2016, 11 (4) : 627-653. doi: 10.3934/nhm.2016012 |
[3] |
Zhi-Qiang Shao. Lifespan of classical discontinuous solutions to the generalized nonlinear initial-boundary Riemann problem for hyperbolic conservation laws with small BV data: shocks and contact discontinuities. Communications on Pure and Applied Analysis, 2015, 14 (3) : 759-792. doi: 10.3934/cpaa.2015.14.759 |
[4] |
Constantine M. Dafermos. A variational approach to the Riemann problem for hyperbolic conservation laws. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 185-195. doi: 10.3934/dcds.2009.23.185 |
[5] |
Yu Zhang, Yanyan Zhang. Riemann problems for a class of coupled hyperbolic systems of conservation laws with a source term. Communications on Pure and Applied Analysis, 2019, 18 (3) : 1523-1545. doi: 10.3934/cpaa.2019073 |
[6] |
Matilde Martínez, Shigenori Matsumoto, Alberto Verjovsky. Horocycle flows for laminations by hyperbolic Riemann surfaces and Hedlund's theorem. Journal of Modern Dynamics, 2016, 10: 113-134. doi: 10.3934/jmd.2016.10.113 |
[7] |
Tong Li, Nitesh Mathur. Riemann problem for a non-strictly hyperbolic system in chemotaxis. Discrete and Continuous Dynamical Systems - B, 2022, 27 (4) : 2173-2187. doi: 10.3934/dcdsb.2021128 |
[8] |
Zhanying Yang. Homogenization and correctors for the hyperbolic problems with imperfect interfaces via the periodic unfolding method. Communications on Pure and Applied Analysis, 2014, 13 (1) : 249-272. doi: 10.3934/cpaa.2014.13.249 |
[9] |
Jean Louis Woukeng. $\sum $-convergence and reiterated homogenization of nonlinear parabolic operators. Communications on Pure and Applied Analysis, 2010, 9 (6) : 1753-1789. doi: 10.3934/cpaa.2010.9.1753 |
[10] |
Eun Heui Kim, Charis Tsikkou. Two dimensional Riemann problems for the nonlinear wave system: Rarefaction wave interactions. Discrete and Continuous Dynamical Systems, 2017, 37 (12) : 6257-6289. doi: 10.3934/dcds.2017271 |
[11] |
Tran Bao Ngoc, Nguyen Huy Tuan, R. Sakthivel, Donal O'Regan. Analysis of nonlinear fractional diffusion equations with a Riemann-liouville derivative. Evolution Equations and Control Theory, 2022, 11 (2) : 439-455. doi: 10.3934/eect.2021007 |
[12] |
Tatsien Li, Wancheng Sheng. The general multi-dimensional Riemann problem for hyperbolic systems with real constant coefficients. Discrete and Continuous Dynamical Systems, 2002, 8 (3) : 737-744. doi: 10.3934/dcds.2002.8.737 |
[13] |
Anupam Sen, T. Raja Sekhar. Structural stability of the Riemann solution for a strictly hyperbolic system of conservation laws with flux approximation. Communications on Pure and Applied Analysis, 2019, 18 (2) : 931-942. doi: 10.3934/cpaa.2019045 |
[14] |
Weishi Liu. Multiple viscous wave fan profiles for Riemann solutions of hyperbolic systems of conservation laws. Discrete and Continuous Dynamical Systems, 2004, 10 (4) : 871-884. doi: 10.3934/dcds.2004.10.871 |
[15] |
Gunther Uhlmann, Jian Zhai. Inverse problems for nonlinear hyperbolic equations. Discrete and Continuous Dynamical Systems, 2021, 41 (1) : 455-469. doi: 10.3934/dcds.2020380 |
[16] |
Fabio Camilli, Claudio Marchi. On the convergence rate in multiscale homogenization of fully nonlinear elliptic problems. Networks and Heterogeneous Media, 2011, 6 (1) : 61-75. doi: 10.3934/nhm.2011.6.61 |
[17] |
Frédéric Legoll, William Minvielle. Variance reduction using antithetic variables for a nonlinear convex stochastic homogenization problem. Discrete and Continuous Dynamical Systems - S, 2015, 8 (1) : 1-27. doi: 10.3934/dcdss.2015.8.1 |
[18] |
M. M. Cavalcanti, V.N. Domingos Cavalcanti, D. Andrade, T. F. Ma. Homogenization for a nonlinear wave equation in domains with holes of small capacity. Discrete and Continuous Dynamical Systems, 2006, 16 (4) : 721-743. doi: 10.3934/dcds.2006.16.721 |
[19] |
Qin Wang, Kyungwoo Song. The regularity of sonic curves for the two-dimensional Riemann problems of the nonlinear wave system of Chaplygin gas. Discrete and Continuous Dynamical Systems, 2016, 36 (3) : 1661-1675. doi: 10.3934/dcds.2016.36.1661 |
[20] |
Chun Wang, Tian-Zhou Xu. Stability of the nonlinear fractional differential equations with the right-sided Riemann-Liouville fractional derivative. Discrete and Continuous Dynamical Systems - S, 2017, 10 (3) : 505-521. doi: 10.3934/dcdss.2017025 |
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