The uniqueness of the solution of the Schrodinger equation with discontinuous coefficients

Consider the Schroeodinger equation: - Du(x) - l(x)u + s(x)u = 0, where D is the Laplacian, l(x) > 0 and s(x) is dominated by l(x). We shall extend the celebrated Kato's result on the asymptotic behavior of the solution to the case where l(x) has unbounded discontinuity. The result will be used to establish the limiting absorption principle for a class of reduced wave operators with discontinuous coefficients.Comment: 29 (twenty-nine) pages; no figures; to appear in Reviews of Mathematical Physic

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-

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