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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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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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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Long-time behavior of an angiogenesis model with flux at the tumor boundary [PDF]
, 2012 This paper deals with a nonlinear system of partial differential equations modeling a simplified tumor-induced angiogenesis taking into account only the interplay between tumor angiogenic factors and endothelial cells.
A. Kettemann +12 more
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Uniform boundedness and global existence of solutions for reaction-diffusion systems with a balance law and a full matrix of diffusion coefficients [PDF]
, 2001 The purpose of this paper is to prove uniform boundedness and so global existence of solutions for reaction-diffusion systems with a full matrix of diffusion coefficients satisfying a balance law.
Kouachi, S.
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Coupling the Stokes and Navier-Stokes equations with two scalar nonlinear parabolic equations [PDF]
, 1999 This work deals with a system of nonlinear parabolic equations arising in turbulence modelling. The unknowns are the N components of the velocity field u coupled with two scalar quantities θ and ϕ. The system presents nonlinear turbulent viscosity A(θ, ϕ)
Gómez Mármol, María Macarena +1 more
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Well-posedness for a class of nonlinear degenerate parabolic equations
, 2015 In this paper we obtain well-posedness for a class of semilinear weakly degenerate reaction-diffusion systems with Robin boundary conditions. This result is obtained through a Gagliardo-Nirenberg interpolation inequality and some embedding results for ...
A. Bensoussan +10 more
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Classical solutions of drift-diffusion equations for semiconductor devices: the 2d case [PDF]
, 2006 We regard drift-diffusion equations for semiconductor devices in Lebesgue spaces. To that end we reformulate the (generalized) van Roosbroeck system as an evolution equation for the potentials to the driving forces of the currents of electrons and holes.
Kaiser, Hans-Christoph +2 more
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