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Diferenciálne rovnice v Banachových priestoroch
Differential equations in banach spaces
Event by: Ústav matematiky
Location: Technická 2896/2, Technická 2, Brno-Královo Pole
Talks & discussions
About event
🗣️ Přídešíčíci: Dušan Oberta
🏢 MiStnost: A1/1842
📆 DATUM: 28. 4. 2025 in 14:00
According to one of the well -known results of ordinary differential equations, so -called. Pean's sentence is a sufficient condition in the right side of the right side for the existence of a local solution of the differential equations system:
x '= F (T, X); X (T_0) = X_0.
If the equations are thinking infinitely a lot, the right side is no longer enough. Generally, the connection of the right side does not guarantee the existence of a local ODR solution in the infinity of brown mining areas. This is due to the lack of compactness in these spaces (in the final dimension the set is compact just if it is closed and bounded, but this is definitely not true in an infinite dimension - for example, a unit closed ball is not compact). We imagine the term so -called. The degree of incomparability, we will show its importance in the existential sentences in the ODR in Banach's spaces and we will see that (not) compactness is still our friend :) Finally, if it was not enough, briefly look at fractional differential equations in banach spaces. In short, it will be eer !!
🏢 MiStnost: A1/1842
📆 DATUM: 28. 4. 2025 in 14:00
According to one of the well -known results of ordinary differential equations, so -called. Pean's sentence is a sufficient condition in the right side of the right side for the existence of a local solution of the differential equations system:
x '= F (T, X); X (T_0) = X_0.
If the equations are thinking infinitely a lot, the right side is no longer enough. Generally, the connection of the right side does not guarantee the existence of a local ODR solution in the infinity of brown mining areas. This is due to the lack of compactness in these spaces (in the final dimension the set is compact just if it is closed and bounded, but this is definitely not true in an infinite dimension - for example, a unit closed ball is not compact). We imagine the term so -called. The degree of incomparability, we will show its importance in the existential sentences in the ODR in Banach's spaces and we will see that (not) compactness is still our friend :) Finally, if it was not enough, briefly look at fractional differential equations in banach spaces. In short, it will be eer !!