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Front motion in multi-dimensional viscous conservation laws with stiff source terms driven by mean curvature and variation of front thickness

2003
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Quarterly of Applied Mathematics
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The bistable reaction-diffusion-convection equation dtu + V ■ f(u): = -g(u) + eAu, x G Rn, u £ R (1) is considered. Stationary traveling waves of the above equation are proved to exist when f(u) is symmetric and g(u) is antisymmetric about u = 0. Solutions of initial value problems tend to almost piecewise constant functions within 0{l)e time. The almost constant pieces are separated by sharp interior layers, called fronts. The motion of these fronts is studied by asymptotic expansion. The

doi:10.1090/qam/2019619
fatcat:mc2byk5qxrexlpyzcns2jthgem