Classical Lie symmetries and reductions of a nonisospectral Lax pair
The classical Lie method is applied to a nonisospectral problem associated with a system of partial differential equations in 2+1 dimensions (Maccari A, J. Math. Phys. 39, (1998), 6547-6551).
Ablowitz M. J.+10 more
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A new contraction family for porous medium and fast diffusion equation [PDF]
In this paper, we present a surprising two-dimensional contraction family for porous medium and fast diffusion equations.
Chmaycem, Ghada+2 more
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Existence of solutions for the Keller-Segel model of chemotaxis with measures as initial data
A simple proof of the existence of solutions for the two-dimensional Keller-Segel model with measures with all the atoms less than $8\pi$ as the initial data is given.
Biler, Piotr, Zienkiewicz, Jacek
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Global Existence and Asymptotic Behavior of Solutions to a Chemotaxis-Fluid System on General Bounded Domain [PDF]
In this paper, we investigate an initial-boundary value problem for a chemotaxis-fluid system in a general bounded regular domain $\Omega \subset \mathbb{R}^N$ ($N\in\{2,3\}$), not necessarily being convex.
Jiang, Jie, Wu, Hao, Zheng, Songmu
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Well-posedness of a porous medium flow with fractional pressure in Sobolev spaces
The nonnegative solution for a linear degenerate diffusion transport eqution is proved. As a result, we show the existence and uniqueness of the solution for the fractional porous medium equation in Sobolev spaces $H^\alpha$ with nonnegative initial data,
Xiao, Weiliang, Zhou, Xuhuan
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The impact factors of the risk index and diffusive dynamics of a SIS free boundary model. [PDF]
Tong Y, Ahn I, Lin Z.
europepmc +1 more source
Harnack's inequality for doubly nonlinear equations of slow diffusion type. [PDF]
Bögelein V+3 more
europepmc +1 more source
Optimal coupling for mean field limits
We review recent quantitative results on the approximation of mean field diffusion equations by large systems of interacting particles, obtained by optimal coupling methods.
Bolley, François
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Heterogeneous Diffusion and Nonlinear Advection in a One-Dimensional Fisher-KPP Problem. [PDF]
Palencia JLD, Rahman SU, Redondo AN.
europepmc +1 more source
Higher integrability for doubly nonlinear parabolic systems. [PDF]
Bögelein V, Duzaar F, Scheven C.
europepmc +1 more source