-widths for singularly perturbed problems
Nash-Moser techniques for nonlinear boundary-value problems.
Navier-Stokes equations on unbounded domains with rough initial data
We consider the Navier-Stokes equations in unbounded domains of uniform -type. We construct mild solutions for initial values in certain extrapolation spaces associated to the Stokes operator on these domains. Here we rely on recent results due to Farwig, Kozono and Sohr, the fact that the Stokes operator has a bounded -calculus on such domains, and use a general form of Kato’s method. We also obtain information on the corresponding pressure term.
Necessary conditions for local and global existence to a reaction-diffusion system with fractional derivatives.
Neumann and second boundary value problems for hessian and Gauß curvature flows
Nevanlinna's first fundamental theorem for supertemperatures.
New a priori estimates for nondiagonal strongly nonlinear parabolic systems
We consider nondiagonal elliptic and parabolic systems of equations with quadratic nonlinearities in the gradient. We discuss a new description of regular points of solutions of such systems. For a class of strongly nonlinear parabolic systems, we estimate locally the Hölder norm of a solution. Instead of smallness of the oscillation, we assume local smallness of the Campanato seminorm of the solution under consideration. Theorems about quasireverse Hölder inequalities proved by the author are essentially...
New exact solutions for a reaction-diffusion equation and a quasi-Camassa Holm equation.
New exact solutions of the Brusselator reaction diffusion model using the exp-function method.
New results on the Burgers and the linear heat equations in unbounded domains.
We consider the Burgers equation and prove a property which seems to have been unobserved until now: there is no limitation on the growth of the nonnegative initial datum u0(x) at infinity when the problem is formulated on unbounded intervals, as, e.g. (0 +∞), and the solution is unique without prescribing its behaviour at infinity. We also consider the associate stationary problem. Finally, some applications to the linear heat equation with boundary conditions of Robin type are also given.
New results on the cauchy problem for parabolic systems and equations with strongly non linear sources.
New schemes for a two-dimensional inverse problem with temperature overspecification.
New trends in coupled simulations featuring domain decomposition and metacomputing
In this paper we test the feasibility of coupling two heterogeneous mathematical modeling integrated within two different codes residing on distant sites. A prototype is developed using Schwarz type domain decomposition as the mathematical tool for coupling. The computing technology for coupling uses a CORBA environment to implement a distributed client-server programming model. Domain decomposition methods are well suited to reducing complex physical phenomena into a sequence of parallel subproblems...
New trends in coupled simulations featuring domain decomposition and metacomputing
In this paper we test the feasibility of coupling two heterogeneous mathematical modeling integrated within two different codes residing on distant sites. A prototype is developed using Schwarz type domain decomposition as the mathematical tool for coupling. The computing technology for coupling uses a CORBA environment to implement a distributed client-server programming model. Domain decomposition methods are well suited to reducing complex physical phenomena into a sequence of parallel subproblems...
New unilateral problems in stratigraphy
This work deals with the study of some stratigraphic models for the formation of geological basins under a maximal erosion rate constrain. It leads to introduce differential inclusions of degenerated hyperbolic-parabolic type , where H is the maximal monotonous graph of the Heaviside function and E is a given non-negative function. Firstly, we present the new and realistic models and an original mathematical formulation, taking into account the weather-limited rate constraint in the conservation...
Nitsche mortaring for parabolic initial-boundary value problems.
Non linear schemes for the heat equation in 1D
Inspired by the growing use of non linear discretization techniques for the linear diffusion equation in industrial codes, we construct and analyze various explicit non linear finite volume schemes for the heat equation in dimension one. These schemes are inspired by the Le Potier’s trick [C. R. Acad. Sci. Paris, Ser. I 348 (2010) 691–695]. They preserve the maximum principle and admit a finite volume formulation. We provide a original functional setting for the analysis of convergence of such methods....
Non local reaction-diffusion equations modelling predator-prey coevolution.
In this paper we examine a predator-prey system with a characteristic of the predator subject to mutation. The ultimate equilibrium of the system is found by Maynard-Smith et al. by the so-called ESS (Evolutionary Stable Strategy). Using a system of reaction-diffusion equations with non local terms, we conclude that ESS result for the diffusion coefficient tending to zero, without resorting to any optimization criterion.
Nonanalyticity of solutions to
It is proved that the solution to the initial value problem , u(0,x) = 1/(1+x²), does not belong to the Gevrey class in time for 0 ≤ s < 1. The proof is based on an estimation of a double sum of products of binomial coefficients.
Nonautonomous ultraparabolic equations applied to population dynamics.