This paper investigates the effects of a degenerate diffusion term in reaction–diffusion models u_t= [D(u)u_x]_x + g(u) with Fisher-KPP type g. Both in the case when D(0)=0 and when D(0)=D(1)=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, L.; Marcelli, Cristina. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 195:2(2003), pp. 471-496.
Sharp profiles in degenerate and doubly degenerate Fisher-KPP equations
MARCELLI, Cristina
2003-01-01
Abstract
This paper investigates the effects of a degenerate diffusion term in reaction–diffusion models u_t= [D(u)u_x]_x + g(u) with Fisher-KPP type g. Both in the case when D(0)=0 and when D(0)=D(1)=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).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
