A smoothing property for the -critical NLS equations and an application to blowup theory
A Sobolev-type inequality with applications.
A solid-fluid model with unilateral contact conditions.
A solution method of the Signorini problem.
A solution of nonlinear diffusion problems by semilinear reaction-diffusion systems
This paper deals with nonlinear diffusion problems involving degenerate parabolic problems, such as the Stefan problem and the porous medium equation, and cross-diffusion systems in population ecology. The degeneracy of the diffusion and the effect of cross-diffusion, that is, nonlinearities of the diffusion, complicate its analysis. In order to avoid the nonlinearities, we propose a reaction-diffusion system with solutions that approximate those of the nonlinear diffusion problems. The reaction-diffusion...
A solution of the boundary value problem in heat conduction
A Spatial Model of Tumor Growth with Cell Age, Cell Size, and Mutation of Cell Phenotypes
A model of tumor growth in a spatial environment is analyzed. The model includes proliferating and quiescent compartments of tumor cells indexed by successively mutated cell phenotypes of increasingly proliferative aggressiveness. The model incorporates spatial dependence due to both random motility and directed movement haptotaxis. The model structures tumor cells by both cell age and cell size. The model consists of a system of nonlinear partial differential equations for the compartments of...
A spatially inhomogeneous diffusion problem with strong absorption
We study the asymptotic behaviour () of the solutions of a nonlinear diffusion problem with strong absorption. We prove convergence to the stationary solution in the by means of an appropriate family of sub and supersolutions. In appendix we prove the well posedness of the problem.
A spatially periodic Kuramoto-Sivashinsky equation as a model problem for inclined film flow over wavy bottom.
A special finite element method based on component mode synthesis
The goal of our paper is to introduce basis functions for the finite element discretization of a second order linear elliptic operator with rough or highly oscillating coefficients. The proposed basis functions are inspired by the classic idea of component mode synthesis and exploit an orthogonal decomposition of the trial subspace to minimize the energy. Numerical experiments illustrate the effectiveness of the proposed basis functions.
A spectral estimate for the Dirac operator on Riemannian flows
We give a new upper bound for the smallest eigenvalues of the Dirac operator on a Riemannian flow carrying transversal Killing spinors. We derive an estimate on both Sasakian and 3-dimensional manifolds, and partially classify those satisfying the limiting case. Finally, we compare our estimate with a lower bound in terms of a natural tensor depending on the eigenspinor.
A Spectral Gap Theorem for Dirac Operators with Central Field.
A spectral problem with an indefinite weight for an elliptic system.
A spectral study of an infinite axisymmetric elastic layer
We present here a theoretical study of eigenmodes in axisymmetric elastic layers. The mathematical modelling allows us to bring this problem to a spectral study of a sequence of unbounded self-adjoint operators , , in a suitable Hilbert space. We show that the essential spectrum of is an interval of type and that, under certain conditions on the coefficients of the medium, the discrete spectrum is non empty.
A spectral study of an infinite axisymmetric elastic layer
We present here a theoretical study of eigenmodes in axisymmetric elastic layers. The mathematical modelling allows us to bring this problem to a spectral study of a sequence of unbounded self-adjoint operators An, , in a suitable Hilbert space. We show that the essential spectrum of An is an interval of type and that, under certain conditions on the coefficients of the medium, the discrete spectrum is non empty.
A speculative approach to quantum gravity.
A spherical Harnack inequality for singular solutions of nonlinear elliptic equations
A splitting formula for an electromagnetic diffraction problem.
A splitting theory for the space of distributions
The splitting problem is studied for short exact sequences consisting of countable projective limits of DFN-spaces (*) 0 → F → X → G → 0, where F or G are isomorphic to the space of distributions D'. It is proved that every sequence (*) splits for F ≃ D' iff G is a subspace of D' and that, for ultrabornological F, every sequence (*) splits for G ≃ D' iff F is a quotient of D'
-stability and numerical solution of abstract differential equations