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Long-time dynamics of an integro-differential equation describing the evolution of a spherical flame.

Hélène Rouzaud (2003)

Revista Matemática Complutense

This article is devoted to the study of a flame ball model, derived by G. Joulin, which satisfies a singular integro-differential equation. We prove that, when radiative heat losses are too important, the flame always quenches; when heat losses are smaller, it stabilizes or quenches, depending on an energy input parameter. We also examine the asymptotics of the radius for these different regimes.

Mathematical analysis of the discharge of a laminar hot gas in a colder atmosphere.

Stanislav Antontsev, Jesús Ildefonso Díaz (2007)

RACSAM

We study the boundary layer approximation of the, already classical, mathematical model which describes the discharge of a laminar hot gas in a stagnant colder atmosphere of the same gas. We start by proving the existence and uniqueness of solutions of the nondegenerate problem under assumptions implying that the temperature T and the horizontal velocity u of the gas are strictly positive: T ≥ δ > 0 and u ≥ ε > 0 (here δ and ε are given as boundary conditions in the external atmosphere)....

Mathematical modelling of cable stayed bridges: existence, uniqueness, continuous dependence on data, homogenization of cable systems

Josef Malík (2004)

Applications of Mathematics

A model of a cable stayed bridge is proposed. This model describes the behaviour of the center span, the part between pylons, hung on one row of cable stays. The existence, the uniqueness of a solution of a time independent problem and the continuous dependence on data are proved. The existence and the uniqueness of a solution of a linearized dynamic problem are proved. A homogenizing procedure making it possible to replace cables by a continuous system is proposed. A nonlinear dynamic problem connected...

Monge solutions for discontinuous hamiltonians

Ariela Briani, Andrea Davini (2005)

ESAIM: Control, Optimisation and Calculus of Variations

We consider an Hamilton-Jacobi equation of the form H ( x , D u ) = 0 x ∈ Ω ⊂ ℝ N , ( 1 ) where H ( x , p ) is assumed Borel measurable and quasi-convex in p . The notion of Monge solution, introduced by Newcomb and Su, is adapted to this setting making use of suitable metric devices. We establish the comparison principle for Monge sub and supersolution, existence and uniqueness for equation (1) coupled with Dirichlet boundary conditions, and a stability result. The relation among Monge and Lipschitz subsolutions is also discussed.

Monge solutions for discontinuous Hamiltonians

Ariela Briani, Andrea Davini (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider an Hamilton-Jacobi equation of the form

 H ( x , D u ) = 0 x ∈ Ω ⊂ ℝ N , ( 1 ) 
 where H(x,p) is assumed Borel measurable and quasi-convex in p. The notion of Monge solution, introduced by Newcomb and Su, is adapted to this setting making use of suitable metric devices. We establish the comparison principle for Monge sub and supersolution, existence and uniqueness for equation ([see full text]) coupled with Dirichlet boundary conditions, and a stability result. The relation among Monge and Lipschitz subsolutions is also...

Monotonicity and symmetry of solutions of p -Laplace equations, 1 < p < 2 , via the moving plane method

Lucio Damascelli, Filomena Pacella (1998)

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

We present some monotonicity and symmetry results for positive solutions of the equation - div ⁢ D ⁢ u p - 2 ⁢ D ⁢ u = f ⁢ u satisfying an homogeneous Dirichlet boundary condition in a bounded domain Ω . We assume 1 < p < 2 and f locally Lipschitz continuous and we do not require any hypothesis on the critical set of the solution. In particular we get that if Ω is a ball then the solutions are radially symmetric and strictly radially decreasing.

Multiplicity bounds for Steklov eigenvalues on Riemannian surfaces

Mikhail Karpukhin, Gerasim Kokarev, Iosif Polterovich (2014)

Annales de l’institut Fourier

We prove two explicit bounds for the multiplicities of Steklov eigenvalues σ k on compact surfaces with boundary. One of the bounds depends only on the genus of a surface and the index k of an eigenvalue, while the other depends as well on the number of boundary components. We also show that on any given Riemannian surface with smooth boundary the multiplicities of Steklov eigenvalues σ k are uniformly bounded in k .

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