Diffusion–convection reaction equations with sign-changing diffusivity and bistable reaction term. (October 2022)

• Record Type: Journal Article
• Authors: Berti, Diego; Corli, Andrea; Malaguti, Luisa
• Is Part Of: Nonlinear analysis. Volume 67(2022)
• Publication Date: 2022-10
• Subjects: Sign-changing diffusivity -- Bistable reaction term -- Diffusion–convection reaction equations -- Traveling-wave solutions -- Sharp profiles; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103579
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We consider a reaction–diffusion equation with a convection term in one space variable, where the diffusion changes sign from the positive to the negative and the reaction term is bistable. We study the existence of wavefront solutions, their uniqueness and regularity. The presence of convection reveals several new features of wavefronts: according to the mutual positions of the diffusivity and reaction, profiles can occur either for a single value of the speed or for a bounded interval of such values; uniqueness (up to shifts) is lost; moreover, plateaus of arbitrary length can appear; profiles can be singular where the diffusion vanishes.