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On a diphasic low mach number system

Stéphane Dellacherie (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We propose a Diphasic Low Mach Number (DLMN) system for the modelling of diphasic flows without phase change at low Mach number, system which is an extension of the system proposed by Majda in [Center of Pure and Applied Mathematics, Berkeley, report No. 112] and [Combust. Sci. Tech.42 (1985) 185–205] for low Mach number combustion problems. This system is written for a priori any equations of state. Under minimal thermodynamic hypothesis which are satisfied by a large class of generalized van...

On a fourth order equation in 3-D

Xingwang Xu, Paul C. Yang (2002)

ESAIM: Control, Optimisation and Calculus of Variations

In this article we study the positivity of the 4-th order Paneitz operator for closed 3-manifolds. We prove that the connected sum of two such 3-manifold retains the same positivity property. We also solve the analogue of the Yamabe equation for such a manifold.

On a Fourth Order Equation in 3-D

Xingwang Xu, Paul C. Yang (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this article we study the positivity of the 4-th order Paneitz operator for closed 3-manifolds. We prove that the connected sum of two such 3-manifold retains the same positivity property. We also solve the analogue of the Yamabe equation for such a manifold.

On a functional equation arising in the kinetic theory of gases

Leif Arkeryd, Carlo Cercignani (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The problem of finding the summational collision invariants for the Boltzmann equation leads to a functional equation related to the Cauchy equation. The solution of this equation is known under different assumptions on its unknown ψ . Most proofs assume that the equation is pointwise satisfied, while the result needed in kinetic theory concerns the solutions of the equation when the latter is satisfied almost everywhere. The only results of this kind appear to be due to the authors of the present...

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