Haraux Alain - Academia.edu (original) (raw)
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Papers by Haraux Alain
Lecture Notes in Mathematics, 1981
Lecture Notes in Mathematics, 1981
Lecture Notes in Mathematics, 1981
Lecture Notes in Mathematics, 1981
Lecture Notes in Mathematics, 1981
Lecture Notes in Mathematics, 1981
Lecture Notes in Mathematics, 1981
Lecture Notes in Mathematics, 1981
Lecture Notes in Mathematics, 1981
Lecture Notes in Mathematics, 1981
Revista Matemática Iberoamericana, 1985
Communications on Pure and Applied Analysis, 2012
ABSTRACT The survey paper presents convergence results for gradient-like systems u ' ... more ABSTRACT The survey paper presents convergence results for gradient-like systems u ' +∇F(u)=0, where F∈C 2 (ℝ N ,ℝ). If u(t) is a bounded solution to this equation for t≥0, then lim t→+∞ dist(u(t),ℰ)=0,whereℰ={a∈ℝ N |∇F=0}· S. Łojasiewicz proved a convergence result for analytic F [Ensembles semi-analytiques. Bures-sur-Yvette: Institut des Hautes Etudes Scientifiques (1965)]. Using a uniform version of the gradient inequality and deriving first energy estimates the author obtains directly convergence and the rate of convergence. A short idea of the state of the art without technical details is also given.
Applicable Analysis, 2014
ABSTRACT We study the asymptotic behavior of solutions of the problemwhere is a convex function w... more ABSTRACT We study the asymptotic behavior of solutions of the problemwhere is a convex function which is bounded from below, with and . This work improves and generalizes some results of the work of Cabot and Frankel [1], where the case was studied.
Lecture Notes in Mathematics, 1981
Lecture Notes in Mathematics, 1981
Lecture Notes in Mathematics, 1981
Lecture Notes in Mathematics, 1981
Lecture Notes in Mathematics, 1981
Lecture Notes in Mathematics, 1981
Lecture Notes in Mathematics, 1981
Lecture Notes in Mathematics, 1981
Lecture Notes in Mathematics, 1981
Lecture Notes in Mathematics, 1981
Revista Matemática Iberoamericana, 1985
Communications on Pure and Applied Analysis, 2012
ABSTRACT The survey paper presents convergence results for gradient-like systems u ' ... more ABSTRACT The survey paper presents convergence results for gradient-like systems u ' +∇F(u)=0, where F∈C 2 (ℝ N ,ℝ). If u(t) is a bounded solution to this equation for t≥0, then lim t→+∞ dist(u(t),ℰ)=0,whereℰ={a∈ℝ N |∇F=0}· S. Łojasiewicz proved a convergence result for analytic F [Ensembles semi-analytiques. Bures-sur-Yvette: Institut des Hautes Etudes Scientifiques (1965)]. Using a uniform version of the gradient inequality and deriving first energy estimates the author obtains directly convergence and the rate of convergence. A short idea of the state of the art without technical details is also given.
Applicable Analysis, 2014
ABSTRACT We study the asymptotic behavior of solutions of the problemwhere is a convex function w... more ABSTRACT We study the asymptotic behavior of solutions of the problemwhere is a convex function which is bounded from below, with and . This work improves and generalizes some results of the work of Cabot and Frankel [1], where the case was studied.