Special Solutions to a Nonlinear Coarsening Model with Local Interactions

Bonforte, M., Vazquez, J.L.: Global positivity estimates and Harnack inequalities for the fast diffusion equation. J. Funct. Anal. 240(2), 399–428 (2006)

Esedoglu, S., Greer, J.B.: Upper bounds on the coarsening rate of discrete, ill-posed nonlinear diffusion equations. Commun. Pure Appl. Math. 62(1), 57–81 (2009)

Esedoglu, S., Slepčev, D.: Refined upper bounds on the coarsening rate of discrete, ill-posed diffusion equations. Nonlinearity 21(12), 2759 (2008)

Giacomin, G., Olla, S., Spohn, H.: Equilibrium Fluctuations for $$\nabla _{\varphi }$$ ∇ φ Interface Model. Ann. Probab. 29(3), 1138–1172, 07 (2001)

Glasner, K.B., Witelski, T.P.: Coarsening dynamics of dewetting films. Phys. Rev. E 67, 016302 (2003)

Glasner, K.B., Witelski, T.P.: Collision versus collapse of droplets in coarsening of dewetting thin films. Phys. D Nonlinear Phenom. 209(1), 80–104 (2005). Non-linear dynamics of thin films and fluid interfaces

Hellén, E.K.O., Krug, J.: Coarsening of sand ripples in mass transfer models. Phys. Rev. E 66, 011304 (2002)

Henseler, R., Niethammer, B., Otto, F.: A reduced model for simulating grain growth. In: Colli, Pierluigi, Verdi, Claudio, Visintin, Augusto (eds.) Free Boundary Problems, pp. 177–187. Birkhäuser Basel, Basel (2004)

Helmers, M., Niethammer, B., Velázquez, J.J.L.: Mathematical analysis of a coarsening model with local interactions. J. Nonlinear Sci. 26(5), 1227–1291 (2016)

Kohn, R.V., Otto, F.: Upper bounds on coarsening rates. Commun. Math. Phys. 229(3), 375–395 (2002)

Nash, J.: Continuity of solutions of parabolic and elliptic equations. Am. J. Math. 80(4), 931–954 (1958)

van der Meer, R.M., van der Weele, J.P., Lohse, D.: Bifurcation diagram for compartmentalized granular gases. Phys. Rev. E Cover. Stat. Nonlinear Biol. Soft Matter Phys. 63(061304), 061304-1–061304-9 (2001)