Fast Reaction, Slow Diffusion, and Curve Shortening 论文

1989SIAM Journal on Applied Mathematics引用 302

Advanced Mathematical Modeling in EngineeringNonlinear Partial Differential EquationsDifferential Equations and Numerical Methods

Advanced Mathematical Modeling in Engineering Nonlinear Partial Differential Equations Differential Equations and Numerical Methods

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</head> <body lang=3DES link=3Dblue vlink=3Dpurple style=3D'tab-interval:35.4pt'> <div class=3DSection1> RESUMEN<o:p></o:p> </div> <![if !vml]><img width=3D96 height=3D24 src=3D"RESUMEN_archivos/image002.gif" v:shapes=3D"_x0000_i1027"><![endif]><![if !vml]><img width=3D96 height=3D24 src=3D"RESUMEN_archivos/image004.gif" v:shapes=3D"_x0000_i1026"><![endif]><![if !vml]><img width=3D96 height=3D24 src=3D"RESUMEN_archivos/image006.gif" v:shapes=3D"_x0000_i1025"><![endif]>The reaction-diffusion problem Ut =3D <a name=3D"OLE_LINK19"></a><a name=3D"OLE_LINK18">ε</a> ∆ U - <a name=3D"OLE_LINK33"></a><a name=3D"OLE_LINK32"> </a><a name=3D"OLE_LINK27"></a><a name=3D"OLE_LINK24"></a><a name=3D"OLE_LINK21"></a><a name=3D"OLE_LINK20">ε</a> -1 Vu (u), u (x, 0, <a name=3D"OLE_LINK29"></a><a name=3D"OLE_LINK28">ε</a>) =3D g (x), <a name=3D"OLE_LINK23"></a><a name=3D"OLE_LINK22">ð</a> n u =3D 0 on <a name=3D"OLE_LINK31"></a><a name=3D"OLE_LINK30">ð </a><a name=3D"OLE_LINK26"></a><a name=3D"OLE_LINK25">Ω</a> for a vector u( x, t, ε) is considered in a domain Ω R m. An asymptotic solution is constructed for ε small. It shows that at each x, u tends quickly to a minimum of V( u ). When V has several minima, u tends to a piecewise constant function. Boundary layer expansions are constructed around the resulting surfaces of discontinuity or fronts. Each front is found to move along its normal with a constant velocity determined by the discontinuity [ V ] in V across it. When [ V ] =3D 0, the front's normal velocity is ε k, where k is its mean curvature. The motion of fronts in this manner is studied for arcs in the plane which are normal to ð Ω at their endpoints, and for fronts that are closed curves. It is shown a front can shrink to a point in a finite time or tend to a locally shortest diameter of Ω. In the latter case, a nonconstant steady state u ( x, ∞, ε) results. Principio del formulario<o:p></o:p> </div> </div> </body> </html>

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Joseph B. Keller

Peter Sternberg

Jacob Rubinstein

Fast Reaction, Slow Diffusion, and Curve Shortening 论文

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