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Convergence of Solutions of Second-Order Gradient-Like Systems with Analytic Nonlinearities

✍ Scribed by A. Haraux; M.A. Jendoubi

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
195 KB
Volume
144
Category
Article
ISSN
0022-0396

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✦ Synopsis

We consider the second-order gradient-like system

where F : R N Γ„ R is analytic and g: R N Γ„ R N is Lipschitz and coercive with g(0)=0.

We prove the convergence of global and bounded solutions of (1) to some equilibrium points.

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The radius of analyticity of periodic analytic functions can be characterized by the decay of their Fourier coefficients. This observation has led to the use of socalled Gevrey norms as a simple way of estimating the time evolution of the spatial radius of analyticity of solutions to parabolic as we