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Gradient estimates for degenerate diffusion equations. I
Mathematische Annalen, 1982 SynopsisWe establish upper and lower bounds for various norms of solutions and their gradients for the equation ut = div (|∇u|m−1 ∇u) in ℝN in terms of the norms of the initial data. Based on the L∞ estimate of ∇u, we conclude that u(x, t) is Lipschitz continuous in space-time, for all t>0, whenever u(x,0) is in L1(ℝN).
Nicholas D Alikakos
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Influence of a nonlinear degenerate diffusion on an advection-diffusion equation in a diffuse interface framework* [PDF]
ESAIM: Proceedings and Surveys, 2023 This work is motivated by the modelling a liquid-vapour flows with phase transition describing the evolution of the coolant within an heat exchanger (e.g. the core of a Pressurized Water Reactor).
Faccanoni Gloria, Galusinski Cédric
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DIFFUSE DEGENERATION OF THE SPINAL CORD [PDF]
The Journal of Nervous and Mental Disease, 1901 n ...
Putnam, James J., Taylor, E. W.
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Doubly degenerate diffuse interface models of surface diffusion [PDF]
Mathematical Methods in the Applied Sciences, 2020 We discuss two doubly degenerate Cahn–Hilliard (DDCH) models for isotropic surface diffusion. Degeneracy is introduced in both the mobility function and a restriction function associated to the chemical potential. Our computational results suggest that the restriction functions yield more accurate approximations of surface diffusion.
Salvalaglio, Marco +2 more
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Indirect Diffusion Effect in Degenerate Reaction-Diffusion Systems [PDF]
SIAM Journal on Mathematical Analysis, 2020 In this work we study global well-posedness and large time behaviour for a typical reaction--diffusion system, which include degenerate diffusion, and whose non-linearities arise from chemical reactions. We show that there is an {\it indirect diffusion effect}, i.e. an effective diffusion for the non-diffusive species which is incurred by a combination
Amit Einav +2 more
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Degenerate diffusion with Preisach hysteresis
Discrete and Continuous Dynamical Systems - S, 2023 34 ...
Gavioli, Chiara, Krejčí, Pavel
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Global existence and asymptotic behavior for a nonlinear degenerate SIS model [PDF]
Opuscula Mathematica, 2013 In this paper we investigate the global existence and asymptotic behavior of a reaction diffusion system with degenerate diffusion arising in the modeling and the spatial spread of an epidemic disease.
Tarik Ali Ziane
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Drift-diffusion models for the simulation of a graphene field effect transistor
Journal of Mathematics in Industry, 2022 A field effect transistor having the active area made of monolayer graphene is simulated by a drift-diffusion model coupled with the Poisson equation. The adopted geometry, already proposed in (Nastasi and Romano in IEEE Trans. Electron.
Giovanni Nastasi, Vittorio Romano
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A Strong Maximum Principle for Nonlinear Nonlocal Diffusion Equations
Axioms, 2023 We consider a class of nonlinear integro-differential equations that model degenerate nonlocal diffusion. We investigate whether the strong maximum principle is valid for this nonlocal equation. For degenerate parabolic PDEs, the strong maximum principle
Tucker Hartland, Ravi Shankar
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Optimal control for a two-sidedly degenerate aggregation equation
Nonlinear Analysis, 2023 In this paper, we are concerned with the study of the mathematical analysis for an optimal control of a nonlocal degenerate aggregation model. This model describes the aggregation of organisms such as pedestrian movements, chemotaxis, animal swarming ...
Mostafa Bendahmane +4 more
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