Propriétés Régularisantes de Certains Semi-Groupes Non Linéaires

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Abstract

Let φ be a convex l.s.c. function from H (Hilbert) into ] - ∞, ∞ ] and D(φ)={u ∈H; φ(u)<+∞}. It is proved that for every u 0 ∈D(φ) the equation - (du/dt)(t ∈ ∂φ(u(t)), u(0)=u 0 has a solution satisfying ÷(du(t)/dt)÷ ≦(c 1/t)+c 2. The behavior of u(t) in the neighborhood of t=0 and t=+∞ as well as the inhomogeneous equation (du(t)/dt)+∂φ(u(t)) ∈f(t) are then studied. Solutions of some nonlinear boundary value problems are given as applications.

Original languageFrench
Pages (from-to)513-534
Number of pages22
JournalIsrael Journal of Mathematics
Volume9
Issue number4
DOIs
StatePublished - Feb 1 1971
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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