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Diffusion phenomenon for second order linear evolution equations

Ryo Ikehata, Kenji Nishihara (2003)

Studia Mathematica

We present an abstract theory of the diffusion phenomenon for second order linear evolution equations in a Hilbert space. To derive the diffusion phenomenon, a new device developed in Ikehata-Matsuyama [5] is applied. Several applications to damped linear wave equations in unbounded domains are also given.

Directional transition matrix

Hiroshi Kokubu, Konstantin Mischaikow, Hiroe Oka (1999)

Banach Center Publications

We present a generalization of topological transition matrices introduced in [6].

Dirichlet boundary value problem for an impulsive forced pendulum equation with viscous and dry frictions

Martina Pavlačková, Pavel Ženčák (2021)

Applications of Mathematics

Sufficient conditions are given for the solvability of an impulsive Dirichlet boundary value problem to forced nonlinear differential equations involving the combination of viscous and dry frictions. Apart from the solvability, also the explicit estimates of solutions and their derivatives are obtained. As an application, an illustrative example is given, and the corresponding numerical solution is obtained by applying Matlab software.

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