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TZID:Europe/Budapest
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UID:6bfdj4m9d8hj577ru544mh4rr4@google.com
CATEGORIES:{lang hu}Differenciálegyenletek szeminárium{/lang}{lang en}Differential equations seminar{/lang}
SUMMARY:Krisztin Tibor: Simasági problémák
LOCATION:Bolyai Intézet, I. emelet, Riesz terem, Aradi Vértanúk tere 1., Szeged
DESCRIPTION;ENCODING=QUOTED-PRINTABLE:Abstract. For differential equations with state-dependent delays a satisfac
tory theory
is developed by H.-O. Walther on the so called solution man
ifold to guarantee $C^1$-smoothness for the solution operators. We present
examples showing that better than $C^1$-smoothness cannot be expected in ge
neral for the solution manifold and for local stable manifolds at stationar
y points on the solution manifold.
Then we propose a new approach to ov
ercome the difficulties caused by the lack of smoothness. The mollification
technique is used to approximate the nonsmooth evaluation map with smooth
maps. Several examples show that the mollified systems can have nicer smoot
hness properties than the original equation. Examples are also given where
better smoothness than $C^1$ can be obtained on the solution manifold.
DTSTAMP:20240328T132352Z
DTSTART;TZID=Europe/Budapest:20170216T100000
DTEND;TZID=Europe/Budapest:20170216T120000
SEQUENCE:0
TRANSP:OPAQUE
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