This paper investigates the effects of a degenerate diffusion term in reaction-diffusion models ut=[D(u)ux]x + g(u) with Fisher-KPP type g. Both in the case when D(0) = 0 and when D(0) = D(l) = 0, with D(u) > 0 elsewhere, we obtain a continuum of travelling wave solutions having wave speed c greater than a threshold value c* and we show the appearance of a sharp-type profile when c = c*. These results solve recent conjectures formulated by Sanchez-Garduno and Maini (J. Differential Equations 117 (1995) 281) and Satnoianu et al. (Discrete Continuous Dyn. Systems (Series B) 1 (2000) 339).
Sharp profiles in degenerate and doubly-degenerate Fisher-KPP equations / Malaguti, Luisa; C., Marcelli. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 195:2(2003), pp. 471-496. [10.1016/j.jde.2003.06.005]
Sharp profiles in degenerate and doubly-degenerate Fisher-KPP equations
MALAGUTI, Luisa;
2003
Abstract
This paper investigates the effects of a degenerate diffusion term in reaction-diffusion models ut=[D(u)ux]x + g(u) with Fisher-KPP type g. Both in the case when D(0) = 0 and when D(0) = D(l) = 0, with D(u) > 0 elsewhere, we obtain a continuum of travelling wave solutions having wave speed c greater than a threshold value c* and we show the appearance of a sharp-type profile when c = c*. These results solve recent conjectures formulated by Sanchez-Garduno and Maini (J. Differential Equations 117 (1995) 281) and Satnoianu et al. (Discrete Continuous Dyn. Systems (Series B) 1 (2000) 339).
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