Darbo vadovas: dr. M. Skujus Darbą parengė: V. Šumskas

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Presentation transcript:

Laike periodinio šilumos laidumo uždavinio sprendinio asimptotika srityse su kampiniu tašku Darbo vadovas: dr. M. Skujus Darbą parengė: V. Šumskas 2017 balandžio 18 MMK JMK 20

Turinys Uždavinio aptarimas Pagalbiniai rezultatai Sprendinio asimptotika Sprendinio periodiškumas laike

Uždavinys ne iš dangaus nusileido Jį nagrinėjo, pavyzdžiui: V. G. Maz'ya S. A. Nazarov B. A. Plamenevskii [3] V. Maz’ya, S. Nazarov, B. Plamenevskii, Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains, Springer Basel AG, Basel, 2000. [5] S.A. Nazarov, B.A. Plamenevskii, Elliptic boundary value problems in domains with piecewise smooth boundaries, Walter de Gruyter and Co, Berlin, 1994.

Šilumos laidumo uždavinys

Uždavinio sritis - sritis su kampiniu tašku. Nupjautinė funkcija: O 1

Suvedimas į elipsinių uždavinių seką

Suvedimas į elipsinių uždavinių seką

Svorinės Sobolevo erdvės Apibendrintos išvestinės iki eilės imtinai ir baigtinė norma:

Svorinės Sobolevo erdvės Be to, a< b => V_a \in V_b

Pagalbiniai rezultatai

Pagalbiniai rezultatai Beta ne taip jau toil nuo vieneto, o gal pavyktų sprendinio erdvę dar pagilinti?

Sprendinio asimptotika .

Sprendinio asimptotika Be to,

Sprendinio asimptotika su , ir

Jungtinis uždavinys

Laike periodinis uždavinys

Laike periodinis uždavinys 1) 2) 3)

Laike periodinis uždavinys 1) Kada konverguoja erdvėje ?

Laike periodinis uždavinys 2)

Laike periodinis uždavinys 3)

Laike periodinis uždavinys

Darbo rezultatai publikuoti „Asymptotics of a solution to the time-periodic heat equation set in domains with corner points“ Skujus, M. & Šumskas, V. Lith Math J (2016) 56: 552. http://link.springer.com/article/10.1007/s10986-016-9336-x

Literatūra [1] A. Ambrazevičius, A. Domarkas, Matematines fizikos lygtys, Aldorija, Vilnius, 1999. [2] L.C. Evans, Partial Differential Equations, AMS: Graduate School in Mathematics, Vol. 19. [3] V. Maz’ya, S. Nazarov, B. Plamenevskij, Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains (Vol. 1), Springer Basel AG, Basel, 2000. [4] V. Maz’ya, S. Nazarov, B. Plamenevskij, Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains (Vol. 2), Springer Basel AG, Basel, 2000. [5] S.A. Nazarov, B.A. Plamenevskii, Elliptic boundary value problems in domains with piecewise smooth boundaries, Walter de Gruyter and Co, Berlin, 1994. [6] O.A. Ladyzhenskaya, The Boundary Value Problems of Mathematical Physics, Applied Mathematical Sciences, Vol. 49, Berlin-Heidelberg-New-York: Springer Verlag, 1985.

Klausimai ir atsakymai

Ačiū už dėmesį!

Svorinės Sobolevo erdvės Be to,

Jungtinis uždavinys