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A differential equation related to the l p -norms

Jacek Bojarski, Tomasz Małolepszy, Janusz Matkowski (2011)

Annales Polonici Mathematici

Let p ∈ (1,∞). The question of existence of a curve in ℝ₊² starting at (0,0) and such that at every point (x,y) of this curve, the l p -distance of the points (x,y) and (0,0) is equal to the Euclidean length of the arc of this curve between these points is considered. This problem reduces to a nonlinear differential equation. The existence and uniqueness of solutions is proved and nonelementary explicit solutions are given.

A differential inclusion : the case of an isotropic set

Gisella Croce (2005)

ESAIM: Control, Optimisation and Calculus of Variations

In this article we are interested in the following problem: to find a map u : Ω 2 that satisfies D u E a.e. in Ω u ( x ) = ϕ ( x ) x Ω where Ω is an open set of 2 and E is a compact isotropic set of 2 × 2 . We will show an existence theorem under suitable hypotheses on ϕ .

A differential inclusion: the case of an isotropic set

Gisella Croce (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this article we are interested in the following problem: to find a map u : Ω 2 that satisfies D u E a.e. in Ω u ( x ) = ϕ ( x ) x Ω where Ω is an open set of 2 and E is a compact isotropic set of 2 × 2 . We will show an existence theorem under suitable hypotheses on φ.

A differential Puiseux theorem in generalized series fields of finite rank

Mickaël Matusinski (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

We study differential equations F ( y , ... , y ( n ) ) = 0 where F is a formal series in y , y , ... , y ( n ) with coefficients in some field of generalized power series 𝕂 r with finite rank r * . Our purpose is to express the support Supp y 0 , i.e. the set of exponents, of the elements y 0 𝕂 r that are solutions, in terms of the supports of the coefficients of the equation, namely Supp F .

A discrete contact model for crowd motion

Bertrand Maury, Juliette Venel (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: we first define a spontaneous velocity which corresponds to the velocity each individual would like to have in the absence of other people. The actual velocity is then computed as the projection of the spontaneous velocity onto the set of admissible velocities (i.e. velocities which do not violate the non-overlapping constraint). We describe here the...

A discrete contact model for crowd motion

Bertrand Maury, Juliette Venel (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: we first define a spontaneous velocity which corresponds to the velocity each individual would like to have in the absence of other people. The actual velocity is then computed as the projection of the spontaneous velocity onto the set of admissible velocities (i.e. velocities which do not violate the non-overlapping constraint). We describe here...

Currently displaying 21 – 40 of 2814