暂无分享,去创建一个
[1] T. Wanner,et al. Branch interactions and long-term dynamics for the diblock copolymer model in one dimension , 2013 .
[2] Xiaofeng Ren,et al. On energy minimizers of the diblock copolymer problem , 2003 .
[3] K. Kawasaki,et al. Equilibrium morphology of block copolymer melts , 1986 .
[4] Xiaofeng Ren,et al. Droplet solutions in the diblock copolymer problem with skewed monomer composition , 2006 .
[5] G. Dahlquist. Stability and error bounds in the numerical integration of ordinary differential equations , 1961 .
[6] Jacek Cyranka. Existence of globally attracting fixed points of viscous Burgers equation with constant forcing. A computer assisted proof , 2013 .
[7] Jacek Cyranka,et al. Efficient and Generic Algorithm for Rigorous Integration Forward in Time of dPDEs: Part I , 2014, J. Sci. Comput..
[8] Evelyn Sander,et al. Validated Saddle-Node Bifurcations and Applications to Lattice Dynamical Systems , 2016, SIAM J. Appl. Dyn. Syst..
[9] Daniel Wilczak,et al. Heteroclinic Connections Between Periodic Orbits in Planar Restricted Circular Three Body Problem. Part II , 2004 .
[10] Jean-Philippe Lessard,et al. Computation of Smooth Manifolds Via Rigorous Multi-parameter Continuation in Infinite Dimensions , 2016, Found. Comput. Math..
[11] J. Lessard,et al. Rigorous Numerics for ill-posed PDEs: Periodic Orbits in the Boussinesq Equation , 2015, 1509.08648.
[12] Xiaofeng Ren,et al. MANY DROPLET PATTERN IN THE CYLINDRICAL PHASE OF DIBLOCK COPOLYMER MORPHOLOGY , 2007 .
[13] P. Zgliczy'nski,et al. Rigorous numerics for PDEs with indefinite tail: existence of a periodic solution of the Boussinesq equation with time-dependent forcing , 2015, 1504.04535.
[14] Piotr Zgliczynski,et al. Attracting Fixed Points for the Kuramoto-Sivashinsky Equation: A Computer Assisted Proof , 2002, SIAM J. Appl. Dyn. Syst..
[15] SOLUTIONS OF NONLINEAR PLANAR ELLIPTIC PROBLEMS WITH TRIANGLE SYMMETRY , 1997 .
[16] D. Wilczak,et al. Topological method for symmetric periodic orbits for maps with a reversing symmetry , 2004, math/0401145.
[17] Peter W. Bates,et al. The Dynamics of Nucleation for the Cahn-Hilliard Equation , 1993, SIAM J. Appl. Math..
[19] Evelyn Sander,et al. Monte Carlo Simulations for Spinodal Decomposition , 1999 .
[20] J. E. Hilliard,et al. Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .
[21] Daniel Wilczak. The Existence of Shilnikov Homoclinic Orbits in the Michelson System: A Computer Assisted Proof , 2006, Found. Comput. Math..
[22] Thomas Wanner,et al. Spinodal Decomposition for the¶Cahn-Hilliard Equation in Higher Dimensions:¶Nonlinear Dynamics , 2000 .
[23] R. Temam. Infinite Dimensional Dynamical Systems in Mechanics and Physics Springer Verlag , 1993 .
[24] T. Wanner,et al. Topological Analysis of the Diblock Copolymer Equation , 2016 .
[25] P. Zgliczynski,et al. Covering relations, cone conditions and the stable manifold theorem , 2009 .
[26] Marian Gidea,et al. Covering relations for multidimensional dynamical systems , 2004 .
[27] Christian Reinhardt,et al. Computing (Un)stable Manifolds with Validated Error Bounds: Non-resonant and Resonant Spectra , 2016, J. Nonlinear Sci..
[28] Yasumasa Nishiura,et al. Some mathematical aspects of the micro-phase separation in diblock copolymers , 1995 .
[29] M. Grinfeld,et al. Counting stationary solutions of the Cahn–Hilliard equation by transversality arguments , 1995, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.
[30] J. F. Williams,et al. 2D Phase Diagram for Minimizers of a Cahn-Hilliard Functional with Long-Range Interactions , 2011, SIAM J. Appl. Dyn. Syst..
[31] Konstantin Mischaikow,et al. Rigorous A Posteriori Computation of (Un)Stable Manifolds and Connecting Orbits for Analytic Maps , 2013, SIAM J. Appl. Dyn. Syst..
[32] Evelyn Sander,et al. Unexpectedly Linear Behavior for the Cahn-Hilliard Equation , 2000, SIAM J. Appl. Math..
[33] T. Wanner. Computer-assisted equilibrium validation for the diblock copolymer model , 2016 .
[34] P. Fife,et al. Perturbation of doubly periodic solution branches with applications to the Cahn-Hilliard equation , 1997 .
[35] Dirk Blömker,et al. Nucleation in the one-dimensional stochastic Cahn-Hilliard model , 2010 .
[36] T. Wanner. Computer-assisted bifurcation diagram validation and applications in materials science , 2018, Rigorous Numerics in Dynamics.
[37] Konstantin Mischaikow,et al. Rigorous Numerics for the Cahn-Hilliard Equation on the Unit Square , 2008 .
[38] X. Ren,et al. On the Derivation of a Density Functional Theory for Microphase Separation of Diblock Copolymers , 2003 .
[39] Konstantin Mischaikow,et al. Rigorous Numerics for Partial Differential Equations: The Kuramoto—Sivashinsky Equation , 2001, Found. Comput. Math..
[40] Konstantin Mischaikow,et al. Rigorous Numerics for Global Dynamics: A Study of the Swift-Hohenberg Equation , 2005, SIAM J. Appl. Dyn. Syst..
[41] R. Canosa,et al. The parameterization method for invariant manifolds I: manifolds associated to non-resonant subspaces , 2002 .
[42] Konstantin Mischaikow,et al. Rigorous Numerics for Symmetric Connecting Orbits: Even Homoclinics of the Gray-Scott Equation , 2011, SIAM J. Math. Anal..
[43] Christopher McCord. Mappings and homological properties in the Conley index theory , 1988 .
[44] Thomas Wanner,et al. Maximum norms of random sums and transient pattern formation , 2003 .
[45] Xiaofeng Ren,et al. Existence and Stability of Spherically Layered Solutions of the Diblock Copolymer Equation , 2006, SIAM J. Appl. Math..
[46] Thomas Wanner,et al. Spinodal Decomposition for the Cahn–Hilliard Equation in Higher Dimensions.¶Part I: Probability and Wavelength Estimate , 1998 .
[47] Piotr Zgliczynski,et al. Rigorous Numerics for Dissipative Partial Differential Equations II. Periodic Orbit for the Kuramoto–Sivashinsky PDE—A Computer-Assisted Proof , 2004, Found. Comput. Math..
[48] Christian Reinhardt,et al. Fourier–Taylor parameterization of unstable manifolds for parabolic partial differential equations: Formalism, implementation and rigorous validation , 2016, Indagationes Mathematicae.
[49] Juncheng Wei,et al. Single Droplet Pattern in the Cylindrical Phase of Diblock Copolymer Morphology , 2007, J. Nonlinear Sci..
[50] Tomasz Kapela,et al. A Lohner-type algorithm for control systems and ordinary differential inclusions , 2007, 0712.0910.
[51] Thomas Wanner,et al. Structure of the Attractor of the Cahn-hilliard equation on a Square , 2007, Int. J. Bifurc. Chaos.
[52] Amy Novick-Cohen,et al. The viscous Cahn-Hilliard equation: Morse decomposition and structure of the global attractor , 1999 .
[53] Evelyn Sander,et al. The Dynamics of Nucleation in Stochastic Cahn-Morral Systems , 2011, SIAM J. Appl. Dyn. Syst..
[54] J. F. Williams,et al. Validation of the bifurcation diagram in the 2D Ohta–Kawasaki problem , 2017 .
[55] Mark A. Peletier,et al. On the Phase Diagram for Microphase Separation of Diblock Copolymers: An Approach via a Nonlocal Cahn--Hilliard Functional , 2009, SIAM J. Appl. Math..
[56] P. Zgliczynski,et al. Rigorous numerics for dissipative PDEs III. An effective algorithm for rigorous integration of dissipative PDEs , 2010 .
[57] Jacek Cyranka,et al. Existence of Globally Attracting Solutions for One-Dimensional Viscous Burgers Equation with Nonautonomous Forcing - A Computer Assisted Proof , 2014, SIAM J. Appl. Dyn. Syst..
[58] Oono,et al. Cell dynamical system approach to block copolymers. , 1990, Physical review. A, Atomic, molecular, and optical physics.
[59] Warwick Tucker,et al. Fixed points of a destabilized Kuramoto-Sivashinsky equation , 2015, Appl. Math. Comput..