We consider a scalar parabolic equation in one spatial dimension. The equation is constituted by a convective term, a reaction term with one or two equilibria, and a positive diffusivity which can however vanish. We prove the existence and several properties of traveling-wave solutions to such an equation. In particular, we provide a sharp estimate for the minimal speed of the profiles and improve previous results about the regularity of wavefronts. Moreover, we show the existence of an infinite number of semi-wavefronts with the same speed.

Uniqueness and nonuniqueness of fronts for degenerate diffusion-convection reaction equations / Berti, D.; Corli, A.; Malaguti, L.. - In: ELECTRONIC JOURNAL ON THE QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS. - ISSN 1417-3875. - 2020:66(2020), pp. 1-34. [10.14232/ejqtde.2020.1.66]

Uniqueness and nonuniqueness of fronts for degenerate diffusion-convection reaction equations

Berti D.;Malaguti L.
2020

Abstract

We consider a scalar parabolic equation in one spatial dimension. The equation is constituted by a convective term, a reaction term with one or two equilibria, and a positive diffusivity which can however vanish. We prove the existence and several properties of traveling-wave solutions to such an equation. In particular, we provide a sharp estimate for the minimal speed of the profiles and improve previous results about the regularity of wavefronts. Moreover, we show the existence of an infinite number of semi-wavefronts with the same speed.
2020
27-nov-2020
2020
66
1
34
Uniqueness and nonuniqueness of fronts for degenerate diffusion-convection reaction equations / Berti, D.; Corli, A.; Malaguti, L.. - In: ELECTRONIC JOURNAL ON THE QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS. - ISSN 1417-3875. - 2020:66(2020), pp. 1-34. [10.14232/ejqtde.2020.1.66]
Berti, D.; Corli, A.; Malaguti, L.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1223721
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