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Papers by Haraux Alain

Research paper thumbnail of More on asymptotic behavior for solutions of the nonlinear dissipative forced wave equation

Lecture Notes in Mathematics, 1981

Research paper thumbnail of Some nonlinear monotone cases

Lecture Notes in Mathematics, 1981

Research paper thumbnail of The linear case: Hilbertian theory and applications

Lecture Notes in Mathematics, 1981

Research paper thumbnail of Schrödinger and wave equations with a logarithmic nonlinearity

Lecture Notes in Mathematics, 1981

Research paper thumbnail of General results for quasi-autonomous periodic systems

Lecture Notes in Mathematics, 1981

Research paper thumbnail of Theory of monotone operators and applications

Lecture Notes in Mathematics, 1981

Research paper thumbnail of Generalities and local theory

Lecture Notes in Mathematics, 1981

Research paper thumbnail of Some nonlinear, non monotone cases

Lecture Notes in Mathematics, 1981

Research paper thumbnail of Autonomous dissipative systems

Lecture Notes in Mathematics, 1981

Research paper thumbnail of The global existence problem

Lecture Notes in Mathematics, 1981

Research paper thumbnail of Semi-groupes linéaires et equations d'evolution linéaires périodiques

Research paper thumbnail of Behavior at Infinity for a Nonlinear Dissipative Wave-Equation

Research paper thumbnail of Oscillations of Anharmonic Fourier Series and the Wave Equation

Revista Matemática Iberoamericana, 1985

Research paper thumbnail of Some applications of the Łojasiewicz gradient inequality

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.

Research paper thumbnail of Asymptotics for a second-order differential equation with nonautonomous damping and an integrable source term

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.

Research paper thumbnail of Pointwise and

Research paper thumbnail of Thierry Cazenave

Research paper thumbnail of term in Hilbert space

Research paper thumbnail of Amina Chabi

Research paper thumbnail of Osci11ations in the wave equation

Research paper thumbnail of More on asymptotic behavior for solutions of the nonlinear dissipative forced wave equation

Lecture Notes in Mathematics, 1981

Research paper thumbnail of Some nonlinear monotone cases

Lecture Notes in Mathematics, 1981

Research paper thumbnail of The linear case: Hilbertian theory and applications

Lecture Notes in Mathematics, 1981

Research paper thumbnail of Schrödinger and wave equations with a logarithmic nonlinearity

Lecture Notes in Mathematics, 1981

Research paper thumbnail of General results for quasi-autonomous periodic systems

Lecture Notes in Mathematics, 1981

Research paper thumbnail of Theory of monotone operators and applications

Lecture Notes in Mathematics, 1981

Research paper thumbnail of Generalities and local theory

Lecture Notes in Mathematics, 1981

Research paper thumbnail of Some nonlinear, non monotone cases

Lecture Notes in Mathematics, 1981

Research paper thumbnail of Autonomous dissipative systems

Lecture Notes in Mathematics, 1981

Research paper thumbnail of The global existence problem

Lecture Notes in Mathematics, 1981

Research paper thumbnail of Semi-groupes linéaires et equations d'evolution linéaires périodiques

Research paper thumbnail of Behavior at Infinity for a Nonlinear Dissipative Wave-Equation

Research paper thumbnail of Oscillations of Anharmonic Fourier Series and the Wave Equation

Revista Matemática Iberoamericana, 1985

Research paper thumbnail of Some applications of the Łojasiewicz gradient inequality

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.

Research paper thumbnail of Asymptotics for a second-order differential equation with nonautonomous damping and an integrable source term

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.

Research paper thumbnail of Pointwise and

Research paper thumbnail of Thierry Cazenave

Research paper thumbnail of term in Hilbert space

Research paper thumbnail of Amina Chabi

Research paper thumbnail of Osci11ations in the wave equation

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