117,830 research outputs found
Albumin improves stability and longevity of perfluorochemical-perfused hearts
No full text Page H1107: L. D. Segel and J. L. Ensunsa. “Albumin improves stability and longevity of perfluorochemical-perfused hearts.” The stroke work data and CVR units in Table 2 should appear as follows. (See PDF) </jats:p
Albumin improves stability and longevity of perfluorochemical-perfused hearts
No full text Page H1107: L. D. Segel and J. L. Ensunsa. “Albumin improves stability and longevity of perfluorochemical-perfused hearts.” The stroke work data and CVR units in Table 2 should appear as follows. (See PDF) </jats:p
Relative entropy methods for hyperbolic and diffusive limits
No full textWe review the relative entropy method in the context of hyperbolic and diffusive relaxation limits of
entropy solutions for various hyperbolic models. The main example consists of the convergence from
multidimensional compressible Euler equations with friction to the porous medium equation \cite{LT12}.
With small modifications, the arguments used in that case can be adapted to the study of the
diffusive limit from the Euler-Poisson system with friction to the Keller-Segel system \cite{LT13}.
In addition, the --system with friction and the system of viscoelasticity with memory are then reviewed,
again in the case of diffusive limits \cite{LT12}.
Finally, the method of relative entropy is described for the multidimensional stress relaxation model converging to elastodynamics \cite[Section 3.2]{LT06}, one of the first examples of application of the method to hyperbolic relaxation limits
Analysis of countercurrent diffusion exchange in blood vessels of the renal medulla
No full text Page 817: D. J. Marsh and L. A. Segel. "Analysis of countercurrent diffusion exchange in blood vessels of the renal medulla." Page 822, column 2, lines 13 and 14 should read, in lower case roman, paragraphed and run in, "The method used to measure linear flow speed tracks erythrocytes." Page 826, column 1, the equation in footnote 1 should read: (See PDF) Page 826, the figure labeled Fig. 5 is Fig. 6; the figure labeled Fig. 6 is Fig. 5. The legends are correct. </jats:p
Sobolev estimates for the Keller-Segel system and applications to the JKO scheme
No full textWe prove L^{\infty}_{t} W^{1,p} Sobolev estimates in the Keller-Segel system by proving a functional inequality, inspired by the Brezis-Gallouët-Wainger inequality. These estimates are also valid at the discrete level in the Jordan-Kinderlehrer-Otto (JKO) scheme. By coupling this result with the diffusion properties of a functional according to Bakry-Emery theory, we deduce the L^{2}_{t} H^{2}_{x} convergence of the scheme, thereby extending the recent result of Santambrogio and Toshpulatov in the context of the Fokker-Planck equation to the Keller-Segel system
L-infinity estimates for the JKO scheme in parabolic-elliptic Keller-Segel systems
No full textWe prove estimates on the densities that are obtained via the JKO scheme for a general form of a parabolic-elliptic Keller-Segel type system, with arbitrary diffusion, arbitrary mass, and in arbitrary dimension. Of course, such an estimate blows up in finite time, a time proportional to the inverse of the initial norm. This estimate can be used to prove short-time well-posedness for a number of equations of this form regardless of the mass of the initial data. The time of existence of the constructed solutions coincides with the maximal time of existence of Lagrangian solutions without the diffusive term by characteristic methods
L^∞ estimates for the jko scheme in parabolic-elliptic keller-segel systems
No full textWe prove L^∞ estimates on the densities that are obtained via the JKO scheme for a general form of a parabolic-elliptic Keller-Segel type system, with arbitrary diffusion, arbitrary mass, and in arbitrary dimension. Of course, such an estimate blows up in finite time, a time proportional to the inverse of the initial L^∞ norm. This estimate can be used to prove short-time well-posedness for a number of equations of this form regardless of the mass of the initial data. The time of existence of the constructed solutions coincides with the maximal time of existence of Lagrangian solutions without the diffusive term by characteristic methods
Uniqueness of weak solutions to a Keller-Segel-Navier-Stokes model with a logistic source
No full textsummary:We prove a uniqueness result of weak solutions to the Cauchy problem of a Keller-Segel-Navier-Stokes system with a logistic term
Sobolev estimates for the Keller-Segel system and applications to the JKO scheme
No full textWe prove L^{\infty}_{t} W^{1,p} Sobolev estimates in the Keller-Segel system by proving a functional inequality, inspired by the Brezis-Gallouët-Wainger inequality. These estimates are also valid at the discrete level in the Jordan-Kinderlehrer-Otto (JKO) scheme. By coupling this result with the diffusion properties of a functional according to Bakry-Emery theory, we deduce the L^{2}_{t} H^{2}_{x} convergence of the scheme, thereby extending the recent result of Santambrogio and Toshpulatov in the context of the Fokker-Planck equation to the Keller-Segel system
Sobolev estimates for the Keller-Segel system and applications to the JKO scheme
No full textWe prove L^{\infty}_{t} W^{1,p} Sobolev estimates in the Keller-Segel system by proving a functional inequality, inspired by the Brezis-Gallouët-Wainger inequality. These estimates are also valid at the discrete level in the Jordan-Kinderlehrer-Otto (JKO) scheme. By coupling this result with the diffusion properties of a functional according to Bakry-Emery theory, we deduce the L^{2}_{t} H^{2}_{x} convergence of the scheme, thereby extending the recent result of Santambrogio and Toshpulatov in the context of the Fokker-Planck equation to the Keller-Segel system
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