Asymptotic stability of the stationary solution to an initial boundary value problem for the Mullins equation of fourth order | Zendy

Peicheng Zhu | Zendy

Open Access

Asymptotic stability of the stationary solution to an initial boundary value problem for the Mullins equation of fourth order

Author(s) -

Peicheng Zhu

Publication year - 2009

Publication title -

journal of mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.708

H-Index - 119

eISSN - 1089-7658

pISSN - 0022-2488

DOI - 10.1063/1.3227656

Subject(s) - mathematics , mathematical analysis , boundary value problem , norm (philosophy) , initial value problem , infinity , exponential stability , order (exchange) , stationary solution , energy method , physics , finance , nonlinear system , quantum mechanics , political science , law , economics

In the present article we first study the existence of the stationary solution to an initial boundary value problem for the Mullins equation of fourth order, which was proposed by Mullins [“Two-dimensional motion of idealized grain boundaries,” J. Appl. Phys. 27, 900 (1956)] to describe the groove development, due to the surface diffusion, at the grain boundaries of a heated polycrystal. Then employing an energy method we prove that this stationary solution is asymptotically stable in a suitable norm as time goes to infinity.

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