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Properties of translating solutions to mean curvature flow
1.  School of Mathematics, Hunan University, Changsha 410082, China 
2.  Department of Mathematical Sciences, Tsinghua University, Beijing 100084 
[1] 
Daehwan Kim, Juncheol Pyo. Existence and asymptotic behavior of helicoidal translating solitons of the mean curvature flow. Discrete and Continuous Dynamical Systems, 2018, 38 (11) : 58975919. doi: 10.3934/dcds.2018256 
[2] 
Tobias H. Colding and Bruce Kleiner. Singularity structure in mean curvature flow of meanconvex sets. Electronic Research Announcements, 2003, 9: 121124. 
[3] 
Xinqun Mei, Jundong Zhou. The interior gradient estimate of prescribed Hessian quotient curvature equation in the hyperbolic space. Communications on Pure and Applied Analysis, 2021, 20 (3) : 11871198. doi: 10.3934/cpaa.2021012 
[4] 
Diego Castellaneta, Alberto Farina, Enrico Valdinoci. A pointwise gradient estimate for solutions of singular and degenerate pde's in possibly unbounded domains with nonnegative mean curvature. Communications on Pure and Applied Analysis, 2012, 11 (5) : 19832003. doi: 10.3934/cpaa.2012.11.1983 
[5] 
Keisuke Takasao. Existence of weak solution for mean curvature flow with transport term and forcing term. Communications on Pure and Applied Analysis, 2020, 19 (5) : 26552677. doi: 10.3934/cpaa.2020116 
[6] 
Sigurd Angenent. Formal asymptotic expansions for symmetric ancient ovals in mean curvature flow. Networks and Heterogeneous Media, 2013, 8 (1) : 18. doi: 10.3934/nhm.2013.8.1 
[7] 
Liangjun Weng. The interior gradient estimate for some nonlinear curvature equations. Communications on Pure and Applied Analysis, 2019, 18 (4) : 16011612. doi: 10.3934/cpaa.2019076 
[8] 
Chiara Corsato, Franco Obersnel, Pierpaolo Omari, Sabrina Rivetti. On the lower and upper solution method for the prescribed mean curvature equation in Minkowski space. Conference Publications, 2013, 2013 (special) : 159169. doi: 10.3934/proc.2013.2013.159 
[9] 
Dimitra Antonopoulou, Georgia Karali. A nonlinear partial differential equation for the volume preserving mean curvature flow. Networks and Heterogeneous Media, 2013, 8 (1) : 922. doi: 10.3934/nhm.2013.8.9 
[10] 
Zixiao Liu, Jiguang Bao. Asymptotic expansion of 2dimensional gradient graph with vanishing mean curvature at infinity. Communications on Pure and Applied Analysis, , () : . doi: 10.3934/cpaa.2022081 
[11] 
Yoshikazu Giga, Hiroyoshi Mitake, Hung V. Tran. Remarks on large time behavior of levelset mean curvature flow equations with driving and source terms. Discrete and Continuous Dynamical Systems  B, 2020, 25 (10) : 39833999. doi: 10.3934/dcdsb.2019228 
[12] 
Ling Mi. Asymptotic behavior for the unique positive solution to a singular elliptic problem. Communications on Pure and Applied Analysis, 2015, 14 (3) : 10531072. doi: 10.3934/cpaa.2015.14.1053 
[13] 
Giulio Colombo, Luciano Mari, Marco Rigoli. Remarks on mean curvature flow solitons in warped products. Discrete and Continuous Dynamical Systems  S, 2020, 13 (7) : 19571991. doi: 10.3934/dcdss.2020153 
[14] 
Zhengchao Ji. Cylindrical estimates for mean curvature flow in hyperbolic spaces. Communications on Pure and Applied Analysis, 2021, 20 (3) : 11991211. doi: 10.3934/cpaa.2021016 
[15] 
Marie Henry, Danielle Hilhorst, Masayasu Mimura. A reactiondiffusion approximation to an area preserving mean curvature flow coupled with a bulk equation. Discrete and Continuous Dynamical Systems  S, 2011, 4 (1) : 125154. doi: 10.3934/dcdss.2011.4.125 
[16] 
Bhargav Kumar Kakumani, Suman Kumar Tumuluri. Asymptotic behavior of the solution of a diffusion equation with nonlocal boundary conditions. Discrete and Continuous Dynamical Systems  B, 2017, 22 (2) : 407419. doi: 10.3934/dcdsb.2017019 
[17] 
Yinbin Deng, Qi Gao. Asymptotic behavior of the positive solutions for an elliptic equation with Hardy term. Discrete and Continuous Dynamical Systems, 2009, 24 (2) : 367380. doi: 10.3934/dcds.2009.24.367 
[18] 
Jinju Xu. A new proof of gradient estimates for mean curvature equations with oblique boundary conditions. Communications on Pure and Applied Analysis, 2016, 15 (5) : 17191742. doi: 10.3934/cpaa.2016010 
[19] 
Frédéric Abergel, JeanMichel Rakotoson. Gradient blowup in Zygmund spaces for the very weak solution of a linear elliptic equation. Discrete and Continuous Dynamical Systems, 2013, 33 (5) : 18091818. doi: 10.3934/dcds.2013.33.1809 
[20] 
Kin Ming Hui. Existence of selfsimilar solutions of the inverse mean curvature flow. Discrete and Continuous Dynamical Systems, 2019, 39 (2) : 863880. doi: 10.3934/dcds.2019036 
2020 Impact Factor: 1.392
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