Abstract:
New exact regular solutions of the nonlinear-diffusion equation are found. Various types of evolution of certain classes of localized initial perturbations are described. We show that, when a localized distribution in the form of a ring is specified, the instantaneous occurrence of the singularity in its center results from the diffusive spreading.
Citation:
S. N. Aristov, “Exact periodic and localized solutions of the equation ht=Δlnhht=Δlnh”, Prikl. Mekh. Tekh. Fiz., 40:1 (1999), 22–26; J. Appl. Mech. Tech. Phys., 40:1 (1999), 16–19
This publication is cited in the following 7 articles:
A. A. Kosov, È. I. Semenov, “New exact solutions of the diffusion equation with power nonlinearity”, Siberian Math. J., 63:6 (2022), 1102–1116
V. B. Bazarova, V. V. Pukhnachev, “Exact solutions of precursor film equation”, J. Math. Sci., 231:2 (2018), 124–142
V. M. Zhuravlev, “Superposition principle and exact solutions of a nonlinear diffusion
equation”, Theoret. and Math. Phys., 183:1 (2015), 478–490
Handbook of Nonlinear Partial Differential Equations, Second Edition, 2011, 1795
Handbook of Nonlinear Partial Differential Equations, 2003
Oleg V Kaptsov, Igor V Verevkin, “Differential constraints and exact solutions of nonlinear diffusion equations”, J. Phys. A: Math. Gen., 36:5 (2003), 1401
V. M. Zhuravlev, “Exact solutions of the nonlinear diffusion equation $u_t=\Delta\log u+ \lambda u$ in a two-dimensional coordinate space”, Theoret. and Math. Phys., 124:2 (2000), 1082–1093
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