109 research outputs found
On the asymptotic behaviour of solutions to the fractional porous medium equation with variable density
We are concerned with the long time behaviour of solutions to the fractional
porous medium equation with a variable spatial density. We prove that if the
density decays slowly at infinity, then the solution approaches the
Barenblatt-type solution of a proper singular fractional problem. If, on the
contrary, the density decays rapidly at infinity, we show that the minimal
solution multiplied by a suitable power of the time variable converges to the
minimal solution of a certain fractional sublinear elliptic equation.Comment: To appear in DCDS-
The radial curvature of an end that makes eigenvalues vanish in the essential spectrum II
Under the quadratic-decay-conditions of the radial curvatures of an end, we
shall derive growth estimates of solutions to the eigenvalue equation and show
the absence of eigenvalues.Comment: "" in the conditions and should be replaced by
"". in the conclusion of Theorem 1.3
should be replaced by ; trivial miss-calculatio
Mathematical Models of Incompressible Fluids as Singular Limits of Complete Fluid Systems
A rigorous justification of several well-known mathematical models of incompressible fluid flows can be given in terms of singular limits of the scaled Navier-Stokes-Fourier system, where some of the characteristic numbers become small or large enough. We discuss the problem in the framework of global-in-time solutions for both the primitive and the target system. © 2010 Springer Basel AG
Eigenvalue problems associated with Korn's inequalities
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46189/1/205_2004_Article_BF00251798.pd
- …