Temat: integro-differential equations - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Numerical modelling of the competition between the adaptive immune system and virus
Autorzy:: Kolev, M.
Powiązania:: https://bibliotekanauki.pl/articles/206177.pdf
Data publikacji:: 2011
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:: numerical modelling
kinetic theory
active particles
integro-differential equations of Boltzmann type
nonlinear dynamics
virus
adaptive immune system
Opis:: We present and analyze numerically a mathematical model of interactions between adaptive immune system and viral infection. The model is a bilinear system of partial integro-differential equations of Boltzmann type. It is a generalization of the recently proposed kinetic models that consider particular (namely, the cellmediated and the humoral) immune mechanisms used in the fight against viral infections. We use Matlab to solve complicated system of equations, present the results of computer simulations and explain their immunological meaning. The results show that the model can describe in a better way (in comparison with the previous kinetic models) real biological situations and is able to illustrate various methods of therapy.
Źródło:: Control and Cybernetics; 2011, 40, 3; 763-778
0324-8569
Pojawia się w:: Control and Cybernetics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: On some new phenomena in state-constrained optimal control if ODEs as well as PDEs are involved
Autorzy:: Pesch, H. J.
Rund, A.
Wahl, V.
Wendl, S.
Powiązania:: https://bibliotekanauki.pl/articles/969885.pdf
Data publikacji:: 2010
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:: optimal control of partial differential equations
ODE-PDE-constrained optimization
state constraints
non-local state-constraints
integro-state constraints
optimal control problems for integro-differential equations
jump conditions
Opis:: In this paper we investigate a new class of optimal control problems with ODE as well as PDE constraints. We would like to call them "hypersonic rocket car problems", since they were inspired, on the one hand, by the well known rocket car problem from the early days of ODE optimal control, on the other hand by a recently investigated flight path trajectory optimization problem for a hypersonic aircraft. The hypersonic rocket car problems mimic the latter's coupling structure, yet in a strongly simplified form. They can therefore be seen as prototypes of ODE-PDE control problems. Due to their relative simplicity they allow to a certain degree to obtain analytical solutions and insights into the structure of the adjoints, which would currently be unthinkable with complex real life problems. Our main aim is to derive and verify the necessary optimality conditions. Most of the obtained results bear a lot of similarities with state constrained ODE optimal control problems, yet we also observed some new phenomena.
Źródło:: Control and Cybernetics; 2010, 39, 3; 647-660
0324-8569
Pojawia się w:: Control and Cybernetics
Dostawca treści:: Biblioteka Nauki

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