An approximation to a sharp type solution of a density-dependent diffusion equation
- In this paper, we use a perturbation method to obtain an approximation to a saddle-saddle heteroclinic trajectory of an autonomous system of ordinary differential equations (ODEs) arising in the equation $u_t= [(u+\epsilon u^2)u_x]_x+u(1-u)$ in the case of travelling wave solutions (t.w.s.): $ u(x,t) = \phi (x - ct)$. We compare the approximate form of the solution profile and speed thus obtained with the actual solution of the full model and the calculated speed, respectively.
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