Front propagation and phase field theory
The connection between the weak theories for a class of geometric equations and the asymptotics of appropriately rescaled reaction-diffusion equations is rigorously established. Two different scalings are studied. In the first, the limiting geometric equation is a first-order equation; in the second...
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| Veröffentlicht in: | SIAM journal on control and optimization 1993-03, Vol.31 (2), p.439-469 |
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| container_end_page | 469 |
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| container_issue | 2 |
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| container_title | SIAM journal on control and optimization |
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| creator | BARLES, G SONER, H. M SOUGANIDIS, P. E |
| description | The connection between the weak theories for a class of geometric equations and the asymptotics of appropriately rescaled reaction-diffusion equations is rigorously established. Two different scalings are studied. In the first, the limiting geometric equation is a first-order equation; in the second, it is a generalization of the mean curvature equation. Intrinsic definitions for the geometric equations are obtained, and uniqueness under a geometric condition on the initial surface is proved. In particular, in the case of the mean curvature equation, this condition is satisfied by surfaces that are strictly starshaped, that have positive mean curvature, or that satisfy a condition that interpolates between the positive mean curvature and the starshape conditions. |
| doi_str_mv | 10.1137/0331021 |
| format | Article |
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| identifier | ISSN: 0363-0129 |
| ispartof | SIAM journal on control and optimization, 1993-03, Vol.31 (2), p.439-469 |
| issn | 0363-0129 1095-7138 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_745086372 |
| source | SIAM Journals |
| subjects | Applied mathematics Continuum mechanics Differential equations Diffusion Exact sciences and technology Flame research Function theory, analysis Geometry Mathematical methods in physics Mathematical models Partial differential equations Phase transitions Physics Propagation Reaction kinetics Set theory Viscosity |
| title | Front propagation and phase field theory |
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