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Existence of solutions to generalized von Foerster equations with functional dependence

Henryk Leszczyński, Piotr Zwierkowski (2004)

Annales Polonici Mathematici

We prove the existence of solutions to a differential-functional system which describes a wide class of multi-component populations dependent on their past time and state densities and on their total size. Using two different types of the Hale operator, we incorporate in this model classical von Foerster-type equations as well as delays (past time dependence) and integrals (e.g. influence of a group of species).

Exponential stability for Timoshenko model with thermal effect

Luiz Gutemberg Rosário Miranda, Bruno Magalhães Alves (2025)

Applications of Mathematics

We performe an exponential decay analysis for a Timoshenko-type system under the thermal effect by constructing the Lyapunov functional. More precisely, this thermal effect is acting as a mechanism for dissipating energy generated by the bending of the beam, acting only on the vertical displacement equation, different from other works already existing in the literature. Furthermore, we show the good placement of the problem using semigroup theory.

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