Moving boundary problems for time fractional and composition dependent diffusion. (English) Zbl 1302.35473
Summary: Some moving boundary problems are considered for time fractional diffusion and explicit results obtained for the motion of planar boundaries, as well as cylindrical and spherical ones. The problem of spherical growth is generalized to include the case of a concentration dependent diffusion coefficient and solutions obtained for slow growth by the method of matched asymptotic expansions.
MSC:
| 35R37 | Moving boundary problems for PDEs |
| 35R11 | Fractional partial differential equations |
| 76M45 | Asymptotic methods, singular perturbations applied to problems in fluid mechanics |
| 74N25 | Transformations involving diffusion in solids |
Keywords:
moving boundary; time fractional composition dependent diffusion; matched asymptotic expansionsReferences:
| [1] | C. Atkinson, Some asymptotic results for the effect of composition dependent diffusion on the growth rates of precipitate particles. Quarterly Journal of Mechanics and Applied Mathematics 27 (1974), 299-316. http://dx.doi.org/10.1093/qjmam/27.3.299; · Zbl 0293.76049 |
| [2] | C. Atkinson and A. Osseiran, Rational solutions for the time-fractional diffusion equation. SIAM J. Appl. Math. 71 (2011), 92-106. http://dx.doi.org/10.1137/100799307; · Zbl 1222.26011 |
| [3] | C. Atkinson and A. Osseiran, Discrete-space time-fractional processes. Frac. Calc. Appl. Anal. 14, No 2 (2011), 201-232; DOI: 10.2478/s13540-011-0013-9; at http://www.springerlink.com/content/1311-0454/14/2/; · Zbl 1312.60040 |
| [4] | N. Bleisten and R. A. Handelsman, Asymptotic Expansions of Integrals. Dover (1986).; |
| [5] | M. Caputo, Linear model of dissipation whose Q is almost frequency Independent — II. Geophysical J. Royal Astronomic Society 13 (1967), 529-539; Reprinted in: Fract. Calc. Appl. Anal. 11, No 1 (2008), 3-14. http://dx.doi.org/10.1111/j.1365-246X.1967.tb02303.x; · Zbl 1210.65130 |
| [6] | M. Caputo and F. Mainardi, Linear models of dissipation in anelastic solids. Riv. Nuovo Cimento (Ser. II) 1 (1971), 161-198. http://dx.doi.org/10.1007/BF02820620; |
| [7] | F. C. Frank, Radially symmetric phase growth controlled by diffusion. Proceedings of the Royal Society A 201 (1950), 1586-1589.; |
| [8] | C. Zener, Theory of growth of spherical precipitates from solid solution. J. Appl. Phys. 20, (1949), 950-963. http://dx.doi.org/10.1063/1.1698258; |
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