Travelling wavefronts in reaction-diffusion equations with convection effects and non-regular terms

By L. Malaguti, C. Marcelli. 2002

55 citations recorded by the source corpus.

This paper deals with the appearance of monotone bounded travelling wave solutions for a parabolic reaction-diffusion equation which frequently meets both in chemical and biological systems. In particular, we prove the existence of monotone front type solutions for any wave speed c ≥ c* and give an estimate for the threshold value c*. Our model takes into account both of a density dependent diffusion term and of a non-linear convection effect. Moreover, we do not require the main non-linearity g to be a regular C1 function; in particular we are able to treat both the case when g′(0) = 0, giving rise to a degenerate equilibrium point in the phase plane, and the singular case when g′(0) = +∞. Our results generalize previous ones due to Aronson and Weinberger [Adv. Math. 30 (1978), pp. 33–76 ], Gibbs and Murray (see Murray [Mathematical Biology, Springer-Verlag, Berlin, 1993 ]) and McCabe, Leach and Needham [SIAM J. Appl. Math. 59 (1998), pp. 870–899 ]. Finally, we obtain our conclusions by means of a comparison-type technique which was introduced and developed in this framework in a recent paper by the same authors.

Subfields: Applied Mathematics, Numerical Analysis, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/83ffaaa07b916133801ed8a828917f81d3871f17

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Guangyu Zhao
2. Shigui Ruan
3. Pierre Magal
4. Wan-Tong Li

In Numerical Analysis

1. Shigui Ruan
2. Guangyu Zhao

In Public Health, Environmental and Occupational Health

1. Guangyu Zhao
2. Shigui Ruan
3. Wan-Tong Li
4. Junjie Wei
5. Guo Lin
6. Yong-Hong Fan

Citations in the corpus

• Entire solutions in reaction-advection-diffusion equations in cylinders (2008, unknown): “From [3,23,24,33] we know that the advection can influence the”
• Sharp profiles in degenerate and doubly degenerate Fisher-KPP equations (2003, background): “In a recent paper [9] we extended these results to the case of weaker regularity conditions both on g and D; and with the introduction of a nonlinear advection term.”
• Time periodic traveling wave solutions for periodic advection–reaction–diffusion systems (2014, methodology): “[28] L. Malaguti, C. Marcelli, Travelling wavefronts in reaction–diffusion equations with convection effects and nonregular terms, Math.”