A blow up of solutions for a system of Klein-Gordon equations with variable exponent : theoretical and numerical results

• Autorzy: Gözen Sedanur Mazi , Yılmaz Nebi , Pişkin Erhan , Okutmustur Baver

Identyfikatory

DOI

10.14708/ma.v51i2.7225

Warianty tytułu

PL

Wybuch rozwiązań układu równań Kleina-Gordona ze zmiennym wykładnikiem : wyniki teoretyczne i numeryczne

• Języki publikacji: EN

Abstrakty

EN

In this paper, we consider a system of Klein-Gordon equations with variable exponents. The first part of the manuscript is devoted to the proof of the blow up of solutions with negative initial energy under suitable conditions on variable exponents and initial data. The theoretical part is supported by numerical experiments based on P1-finite element method in space and the BDF and the Generalized-alpha methods in time illustrated in the second part. The numerical and analytical results of the blow up solutions agree with each other.

PL

Praca poświęcona jest układowi równań Kleina-Gordona ze zmiennymi wykładnikami. W pierwszej części pokazano, że rozwiązania o ujemnej energii początkowej uciekają do nieskończoności przy odpowiednich warunkach na wykładniki oraz dane początkowe. Część teoretyczną uzupełniają obliczenia numeryczne oparte na metodzie elementu skończonego dla zmiennych przestrzennych oraz metodzie różniczkowania wstecz (Backward Differentiation Formula, BDF). Wyniki numeryczne i analityczne dotyczące wybuchowego charakteru rozwiązań wzajemnie potwierdzają się.

Słowa kluczowe

EN

Blow up; Klein-Gordon equation; Variable exponent; Generalized alpha method; BDF method; P1-finite element method; finite difference method

PL

wybuch; równanie Kleina-Gordona; zmienny wykładnik; formuła wstecznego różniczkowania; metoda elementów skończonych; metoda różnic skończonych

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Mathematica Applicanda
• Rocznik: 2023
• Tom: Vol. 51, no. 2
• Strony: 143--164
• Opis fizyczny: Bibliogr. 23 poz., rys., tab., wykr.

Twórcy

autor

Gözen Sedanur Mazi

• Istanbul Technical University (ITU) in Istanbul

• https://orcid.org/0000-0001-6812-3646+

autor

Yılmaz Nebi

• https://orcid.org/0000-0001-5615-9043

autor

Pişkin Erhan

• Department of Mathematics in Dicle University, Diyarbakir, TR

• https://orcid.org/0000-0001-6587-4479

autor

Okutmustur Baver

• Middle East Technical University (METU) Department of Mathematics, Ankara

• https://orcid.org/0000-0001-9485-205X+

Bibliografia

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• [14] S. A. Messaoudi, O. Bouhoufani, I. Hamchi and M. Alahyane. Existence and Blow up in a system of wave Equations with nonstandard, Nonlinearities Electronic Journal of Differential Equations (91):1–33, 2021.
• [15] S.H. Park and J.R. Kang. Blow-up of solutions for a viscoelastic wave equation with variable exponents, Math. Methods Appl. Sci., 42 (6):2083–2097, 2019.
• [16] E. Pişkin. Global Nonexistence of Solutions for a Nonlinear Klein-Gordon Equation with Variable Exponents, Applied Mathematics Notes, (19):315-323, 2019.
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Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).