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Quasichemical Models of Multicomponent Nonlinear Diffusion

A.N. Gorban, H.P. Sargsyan, H.A. Wahab (2011)

Mathematical Modelling of Natural Phenomena

Diffusion preserves the positivity of concentrations, therefore, multicomponent diffusion should be nonlinear if there exist non-diagonal terms. The vast variety of nonlinear multicomponent diffusion equations should be ordered and special tools are needed to provide the systematic construction of the nonlinear diffusion equations for multicomponent mixtures with significant interaction between components. We develop an approach to nonlinear multicomponent...

Quasineutral limit of the Euler-Poisson system for ions in a domain with boundaries II

David Gérard-Varet, Daniel Han-Kwan, Frédéric Rousset (2014)

Journal de l’École polytechnique — Mathématiques

In this paper, we study the quasineutral limit of the isothermal Euler-Poisson equation for ions, in a domain with boundary. This is a follow-up to our previous work [5], devoted to no-penetration as well as subsonic outflow boundary conditions. We focus here on the case of supersonic outflow velocities. The structure of the boundary layers and the stabilization mechanism are different.

Quasi-periodic solutions with Sobolev regularity of NLS on 𝕋 d with a multiplicative potential

Massimiliano Berti, Philippe Bolle (2013)

Journal of the European Mathematical Society

We prove the existence of quasi-periodic solutions for Schrödinger equations with a multiplicative potential on 𝕋 d , d 1 , finitely differentiable nonlinearities, and tangential frequencies constrained along a pre-assigned direction. The solutions have only Sobolev regularity both in time and space. If the nonlinearity and the potential are C then the solutions are C . The proofs are based on an improved Nash-Moser iterative scheme, which assumes the weakest tame estimates for the inverse linearized operators...

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