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Application des méthodes de convexité et monotonie a l'étude de certaines équations quasi linéaires

Published online by Cambridge University Press:  14 February 2012

H. Attouch  and
A. Damlamian
H. Attouch
Affiliation:
Université de Paris-Sud, 91405 Orsay
A. Damlamian
Affiliation:
Université de Paris-Sud, 91405 Orsay
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Synopsis

Using Hilbert space methods, existence and uniqueness are proved for the solution of some strongly non-linear partial differential equations of elliptic and parabolic type.

They are associated with quasi-linear operators of the form: -div(β(x, grad u)) + β0(x, u) where β (resp β0) is a maximal monotone subdifferential on ℝN(resp ℝ) depending smoothly on x in a bounded domain Ω of ℝN

These operators are shown to be the subdifierentials over Lp(Ω) of convex functional of the following type:

where j is a normal convex integrand over Ω×ℝN+1 satisfying a coerciveness condition.

This method avoids the theory of Sobolev-Orlicz spaces. An application is given also forthe gas-diffusion equation over ℝ+.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 79 , Issue 1-2 , 1977 , pp. 107 - 129
Copyright
Copyright © Royal Society of Edinburgh 1977

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