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Short-time pattern formation in thin film equations
1. | Department of Mathematics, Pohang University of Science and Technology, Pohang 790-784, South Korea |
2. | Mathematics Department, Duke University, Box 90320, Durham, NC 27708-0320, United States |
[1] |
Marina Chugunova, Roman M. Taranets. New dissipated energy for the unstable thin film equation. Communications on Pure and Applied Analysis, 2011, 10 (2) : 613-624. doi: 10.3934/cpaa.2011.10.613 |
[2] |
Eric A. Carlen, Süleyman Ulusoy. Localization, smoothness, and convergence to equilibrium for a thin film equation. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4537-4553. doi: 10.3934/dcds.2014.34.4537 |
[3] |
Richard S. Laugesen. New dissipated energies for the thin fluid film equation. Communications on Pure and Applied Analysis, 2005, 4 (3) : 613-634. doi: 10.3934/cpaa.2005.4.613 |
[4] |
Changchun Liu, Jingxue Yin, Juan Zhou. Existence of weak solutions for a generalized thin film equation. Communications on Pure and Applied Analysis, 2007, 6 (2) : 465-480. doi: 10.3934/cpaa.2007.6.465 |
[5] |
Jian-Guo Liu, Jinhuan Wang. Global existence for a thin film equation with subcritical mass. Discrete and Continuous Dynamical Systems - B, 2017, 22 (4) : 1461-1492. doi: 10.3934/dcdsb.2017070 |
[6] |
Huiqiang Jiang. Energy minimizers of a thin film equation with born repulsion force. Communications on Pure and Applied Analysis, 2011, 10 (2) : 803-815. doi: 10.3934/cpaa.2011.10.803 |
[7] |
Daniel Ginsberg, Gideon Simpson. Analytical and numerical results on the positivity of steady state solutions of a thin film equation. Discrete and Continuous Dynamical Systems - B, 2013, 18 (5) : 1305-1321. doi: 10.3934/dcdsb.2013.18.1305 |
[8] |
Minhajul, T. Raja Sekhar, G. P. Raja Sekhar. Stability of solutions to the Riemann problem for a thin film model of a perfectly soluble anti-surfactant solution. Communications on Pure and Applied Analysis, 2019, 18 (6) : 3367-3386. doi: 10.3934/cpaa.2019152 |
[9] |
R.A. Satnoianu, Philip K. Maini, F.S. Garduno, J.P. Armitage. Travelling waves in a nonlinear degenerate diffusion model for bacterial pattern formation. Discrete and Continuous Dynamical Systems - B, 2001, 1 (3) : 339-362. doi: 10.3934/dcdsb.2001.1.339 |
[10] |
Christian Kuehn, Pasha Tkachov. Pattern formation in the doubly-nonlocal Fisher-KPP equation. Discrete and Continuous Dynamical Systems, 2019, 39 (4) : 2077-2100. doi: 10.3934/dcds.2019087 |
[11] |
Lihua Min, Xiaoping Yang. Finite speed of propagation and algebraic time decay of solutions to a generalized thin film equation. Communications on Pure and Applied Analysis, 2014, 13 (2) : 543-566. doi: 10.3934/cpaa.2014.13.543 |
[12] |
Sergey Degtyarev. Classical solvability of the multidimensional free boundary problem for the thin film equation with quadratic mobility in the case of partial wetting. Discrete and Continuous Dynamical Systems, 2017, 37 (7) : 3625-3699. doi: 10.3934/dcds.2017156 |
[13] |
Cheng Wang, Xiaoming Wang, Steven M. Wise. Unconditionally stable schemes for equations of thin film epitaxy. Discrete and Continuous Dynamical Systems, 2010, 28 (1) : 405-423. doi: 10.3934/dcds.2010.28.405 |
[14] |
P. Álvarez-Caudevilla, J. D. Evans, V. A. Galaktionov. The Cauchy problem for a tenth-order thin film equation II. Oscillatory source-type and fundamental similarity solutions. Discrete and Continuous Dynamical Systems, 2015, 35 (3) : 807-827. doi: 10.3934/dcds.2015.35.807 |
[15] |
Lei Yang, Xiao-Ping Wang. Dynamics of domain wall in thin film driven by spin current. Discrete and Continuous Dynamical Systems - B, 2010, 14 (3) : 1251-1263. doi: 10.3934/dcdsb.2010.14.1251 |
[16] |
Julien Barré, Pierre Degond, Diane Peurichard, Ewelina Zatorska. Modelling pattern formation through differential repulsion. Networks and Heterogeneous Media, 2020, 15 (3) : 307-352. doi: 10.3934/nhm.2020021 |
[17] |
Julien Cividini. Pattern formation in 2D traffic flows. Discrete and Continuous Dynamical Systems - S, 2014, 7 (3) : 395-409. doi: 10.3934/dcdss.2014.7.395 |
[18] |
Yuan Lou, Wei-Ming Ni, Shoji Yotsutani. Pattern formation in a cross-diffusion system. Discrete and Continuous Dynamical Systems, 2015, 35 (4) : 1589-1607. doi: 10.3934/dcds.2015.35.1589 |
[19] |
Peter Rashkov. Remarks on pattern formation in a model for hair follicle spacing. Discrete and Continuous Dynamical Systems - B, 2015, 20 (5) : 1555-1572. doi: 10.3934/dcdsb.2015.20.1555 |
[20] |
Tian Ma, Shouhong Wang. Dynamic transition and pattern formation for chemotactic systems. Discrete and Continuous Dynamical Systems - B, 2014, 19 (9) : 2809-2835. doi: 10.3934/dcdsb.2014.19.2809 |
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