We study a nonlinear reaction-convection equation with a degenerate diffusion of Perona-Malik's type and a monostable reaction term. Under quite general assumptions, we show the presence of wavefront solutions and prove their main properties. In particular, such wavefronts exist for every speed in a closed half-line and we give estimates of the threshold speed. The wavefront profiles are also strictly monotone and their slopes are uniformly bounded by the critical values of the diffusion.
Wavefront solutions to reaction-convection equations with Perona-Malik diffusion / Corli, A.; Malaguti, L.; Sovrano, E.. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 308:(2022), pp. 474-506. [10.1016/j.jde.2021.09.041]
Wavefront solutions to reaction-convection equations with Perona-Malik diffusion
Malaguti L.;Sovrano E.
2022
Abstract
We study a nonlinear reaction-convection equation with a degenerate diffusion of Perona-Malik's type and a monostable reaction term. Under quite general assumptions, we show the presence of wavefront solutions and prove their main properties. In particular, such wavefronts exist for every speed in a closed half-line and we give estimates of the threshold speed. The wavefront profiles are also strictly monotone and their slopes are uniformly bounded by the critical values of the diffusion.
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