[CvGmt News] [cvgmt seminar] The effects of flux-saturated diffusion on indefinite ogistic-growth models

[michele.miranda at unife.it]

The effects of flux-saturated diffusion on indefinite ogistic-growth models
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http://cvgmt.sns.it/seminar/812/

Date: Thursday, May 13, 2021

Time: 16:00

Place: University of Ferrara (on-line)

Speaker: Elisa Sovrano



Abstract. Reaction-diffusion processes can be based on Fick-Fourier's law. Changing perspective, we deal with a dispersive flux which is a nonlinear bounded function of the gradient. In a bounded domain with a regular boundary, we investigate a Dirichlet problem associated with a quasilinear reaction-diffusion equation where the mean curvature operator drives the diffusion process. As for the reaction, we consider the product of a logistic-type nonlinearity and a sign-changing weight function modeling spatial heterogeneities. For this problem, we present some recent results concerning the existence and the multiplicity of positive solutions. Depending on the logistic term's behavior at zero, we prove three qualitatively different bifurcation diagrams by varying the diffusivity parameter. We point out a new multiplicity phenomenon without any similarity with the case of linear-diffusion logistic-growth models. 
This talk is based on joint works with Pierpaolo Omari (University of Trieste).

GoogleMeet link: https://meet.google.com/dif-qrmm-bgy