A further improved tanh function method exactly solving the -dimensional dispersive long wave equations.
A Galerkin strategy with Proper Orthogonal Decomposition for parameter-dependent problems – Analysis, assessments and applications to parameter estimation
We address the issue of parameter variations in POD approximations of time-dependent problems, without any specific restriction on the form of parameter dependence. Considering a parabolic model problem, we propose a POD construction strategy allowing us to obtain some a priori error estimates controlled by the POD remainder – in the construction procedure – and some parameter-wise interpolation errors for the model solutions. We provide a thorough numerical assessment of this strategy with the...
A general approach for multiconfiguration method sin quantum molecular chemistry
A general class of phase transition models with weighted interface energy
A general Hamilton-Jacobi framework for non-linear state-constrained control problems
The paper deals with deterministic optimal control problems with state constraints and non-linear dynamics. It is known for such problems that the value function is in general discontinuous and its characterization by means of a Hamilton-Jacobi equation requires some controllability assumptions involving the dynamics and the set of state constraints. Here, we first adopt the viability point of view and look at the value function as its epigraph. Then, we prove that this epigraph can always be described...
A general perturbation formula for electromagnetic fields in presence of low volume scatterers
In several practically interesting applications of electromagnetic scattering theory like, e.g., scattering from small point-like objects such as buried artifacts or small inclusions in non-destructive testing, scattering from thin curve-like objects such as wires or tubes, or scattering from thin sheet-like objects such as cracks, the volume of the scatterers is small relative to the volume of the surrounding medium and with respect to the wave length of the applied electromagnetic fields. This...
A general perturbation formula for electromagnetic fields in presence of low volume scatterers
In several practically interesting applications of electromagnetic scattering theory like, e.g., scattering from small point-like objects such as buried artifacts or small inclusions in non-destructive testing, scattering from thin curve-like objects such as wires or tubes, or scattering from thin sheet-like objects such as cracks, the volume of the scatterers is small relative to the volume of the surrounding medium and with respect to the wave length of the applied electromagnetic fields. This...
A generalization for Peakon's solitary wave and Camassa-Holm equation.
A generalization of a theorem by Kato on Navier-Stokes equations.
We generalize a classical result of T. Kato on the existence of global solutions to the Navier-Stokes system in C([0,∞);L3(R3)). More precisely, we show that if the initial data are sufficiently oscillating, in a suitable Besov space, then Kato's solution exists globally. As a corollary to this result, we obtain a theory of existence of self-similar solutions for the Navier-Stokes equations.
A generalization of the Keller-Segel system to higher dimensions from a structural viewpoint
We consider initial boundary problems of a two-chemical substances chemotaxis system. In the four-dimensional setting, it was shown that solutions exist globally in time and remain bounded if the total mass is less than , whereas the solution emanating from some initial data of large magnitude may blows up. This result can be regarded as a generalization of the well-known problem in the Keller–Segel system to higher dimensions. We will compare mathematical structures of the Keller–Segel system...
A generalization of the radiation condition of Sommerfeld for -body Schrödinger operators
A geometric derivation of the linear Boltzmann equation for a particle interacting with a Gaussian random field, using a Fock space approach
In this article the linear Boltzmann equation is derived for a particle interacting with a Gaussian random field, in the weak coupling limit, with renewal in time of the random field. The initial data can be chosen arbitrarily. The proof is geometric and involves coherent states and semi-classical calculus.
A geometric improvement of the velocity-pressure local regularity criterion for a suitable weak solution to the Navier-Stokes equations
We deal with a suitable weak solution to the Navier-Stokes equations in a domain . We refine the criterion for the local regularity of this solution at the point , which uses the -norm of and the -norm of in a shrinking backward parabolic neighbourhood of . The refinement consists in the fact that only the values of , respectively , in the exterior of a space-time paraboloid with vertex at , respectively in a ”small” subset of this exterior, are considered. The consequence is that...
A geometrical interpretation of the time evolution of the Schrödinger equation for discrete quantum systems
A Global a posteriori Error Estimate for Quasilinear Elliptic Problems.
A global existence result for the compressible Navier-Stokes-Poisson equations in three and higher dimensions
The paper is dedicated to the global well-posedness of the barotropic compressible Navier-Stokes-Poisson system in the whole space with N ≥ 3. The global existence and uniqueness of the strong solution is shown in the framework of hybrid Besov spaces. The initial velocity has the same critical regularity index as for the incompressible homogeneous Navier-Stokes equations. The proof relies on a uniform estimate for a mixed hyperbolic/parabolic linear system with a convection term.
A global existence result in Sobolev spaces for MHD system in the half-plane
A gradient weighted moving finite-element method with polynomial approximation of any degree.
A Hamilton-Jacobi approach to junction problems and application to traffic flows
This paper is concerned with the study of a model case of first order Hamilton-Jacobi equations posed on a “junction”, that is to say the union of a finite number of half-lines with a unique common point. The main result is a comparison principle. We also prove existence and stability of solutions. The two challenging difficulties are the singular geometry of the domain and the discontinuity of the Hamiltonian. As far as discontinuous Hamiltonians are concerned, these results seem to be new. They...
-harmonic equations and the Dirac operator.