On a property of a classical solution of the nonlinear mass transport equation u t=u x x/1+u x 2
Open Access
- 1 May 1986
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 27 (5) , 1391-1392
- https://doi.org/10.1063/1.527096
Abstract
A mechanism of smoothing due to evaporation–condensation of the roughly perturbed surface of solid is described by Mullins [W. W. Mullins, J. Appl. Phys. 2 8, 333 (1957); 3 0, 77 (1959)] in terms of the Cauchy problem (P) in R1 (real line) of a nonlinear parabolic equation for u(x,t) representing the evolution of the profile of the surface: ut=uxx/1+ux2, (x,t)∈ R1×(0,∞); u(x,0)=α(x), x∈ R1[model (P)]. In the present paper, it is demonstrated that each peak height of the initial surface α(x) in Mullins’ model (P) does not increase with time.Keywords
This publication has 2 references indexed in Scilit:
- Flattening of a Nearly Plane Solid Surface due to CapillarityJournal of Applied Physics, 1959
- Theory of Thermal GroovingJournal of Applied Physics, 1957