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Uniform attractors in sup-norm for semi linear parabolic problem and application to the robust stability theory

Oleksiy Kapustyan, Olena Kapustian, Oleksandr Stanzytskyi, Ihor Korol (2023)

Archivum Mathematicum

In this paper we establish the existence of the uniform attractor for a semi linear parabolic problem with bounded non autonomous disturbances in the phase space of continuous functions. We applied obtained results to prove the asymptotic gain property with respect to the global attractor of the undisturbed system.

Uniform Stability In Nonlinear Infinite Delay Volterra Integro-differential Equations Using Lyapunov Functionals

Youssef Raffoul, Habib Rai (2016)

Nonautonomous Dynamical Systems

In [10] the first author used Lyapunov functionals and studied the exponential stability of the zero solution of finite delay Volterra Integro-differential equation. In this paper, we use modified version of the Lyapunov functional that were used in [10] to obtain criterion for the stability of the zero solution of the infinite delay nonlinear Volterra integro-differential equation [...]

Uniformly enclosing discretization methods and grid generation for semilinear boundary value problems with first order terms

Hans-Görg Roos (1989)

Aplikace matematiky

The paper deals with uniformly enclosing discretization methods of the first order for semilinear boundary value problems. Some fundamental properties of this discretization technique (the enclosing property, convergence, the inverse-monotonicity) are proved. A feedback grid generation principle using information from the lower and upper solutions is presented.

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