The fractional Keller-Segel model [PDF]
, 2006 The Keller-Segel model is a system of partial differential equations modelling chemotactic aggregation in cellular systems. This model has blowing up solutions for large enough initial conditions in dimensions d >= 2, but all the solutions are regular in
Brenner M P +9 more
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Evolution Equations governed by Lipschitz Continuous Non-autonomous Forms [PDF]
, 2014 We prove $L^2$-maximal regularity of linear non-autonomous evolutionary Cauchy problem \begin{equation}\label{eq00}\nonumber \dot{u} (t)+A(t)u(t)=f(t) \hbox{ for }\ \hbox{a.e.
Laasri, Hafida, Sani, Ahmed
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Local existence result of the single dopant diffusion including cluster reactions of high order
Abstract and Applied Analysis, Volume 6, Issue 1, Page 13-34, 2001., 2001 We consider the pair diffusion process which includes cluster reactions of high order. We are able to prove a local (in time) existence result in arbitrary space dimensions. The model includes a nonlinear system of reaction‐drift‐diffusion equations, a nonlinear system of ordinary differential equations in Banach spaces, and a nonlinear elliptic ...
R. Bader, W. Merz
wiley +1 more source
On a 3D isothermal model for nematic liquid crystals accounting for stretching terms [PDF]
, 2012 The present contribution investigates the well-posedness of a PDE system describing the evolution of a nematic liquid crystal flow under kinematic transports for molecules of different shapes. More in particular, the evolution of the {\em velocity field}
Cavaterra, Cecilia, Rocca, Elisabetta
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Backward blow-up estimates and initial trace for a parabolic system of reaction-diffusion [PDF]
, 2010 In this article we study the positive solutions of the parabolic semilinear system of competitive type \[ \left\{\begin{array} [c]{c}% u_{t}-\Delta u+v^{p}=0, v_{t}-\Delta v+u^{q}=0, \end{array} \right.
Bidaut-Véron, Marie-Françoise +2 more
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A cross-diffusion system derived from a Fokker-Planck equation with partial averaging [PDF]
, 2016 A cross-diffusion system for two compoments with a Laplacian structure is analyzed on the multi-dimensional torus. This system, which was recently suggested by P.-L.
Jüngel, Ansgar, Zamponi, Nicola
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Longtime behavior for a generalized Cahn-Hilliard system with fractional operators [PDF]
, 2019 In this contribution, we deal with the longtime behavior of the solutions to the fractional variant of the Cahn-Hilliard system, with possibly singular potentials, that we have recently investigated in the paper `Well-posedness and regularity for a ...
Colli, Pierluigi +2 more
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Non-simultaneous quenching in a system of heat equations coupled at the boundary [PDF]
, 2006 We study the solutions of a parabolic system of heat equations coupled at the boundary through a nonlinear flux. We characterize in terms of the parameters involved when nonsimultaneous quenching may appear.
de Pablo, Arturo +3 more
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Analysis of a model arising from invasion by precursor and differentiated cells
, 2013 We study the wave solutions for a degenerated reaction diffusion system arising from the invasion of cells. We show that there exists a family of waves for the wave speed larger than or equals a certain number, and below which there is no monotonic wave ...
Hou, Xiaojie
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, 2012 The paper deals with reaction-diffusion equations involving a hysteretic discontinuity in the source term, which is defined at each spatial point. Such problems describe biological processes and chemical reactions in which diffusive and nondiffusive ...
Gurevich, Pavel, Tikhomirov, Sergey
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