Local existence for a viscoelastic Kirchhoff type equation with the dispersive term, internal damping, and logarithmic nonlinearity

• Autorzy: Cordeiro Sebastião , Raposo Carlos , Ferreira Jorge , Rocha Daniel , Shahrouzi Mohammad

Identyfikatory

DOI

10.7494/OpMath.2024.44.1.19

• Języki publikacji: EN

Abstrakty

EN

This paper concerns a viscoelastic Kirchhoff-type equation with the dispersive term, internal damping, and logarithmic nonlinearity. We prove the local existence of a weak solution via a modified lemma of contraction of the Banach fixed-point theorem. Although the uniqueness of a weak solution is still an open problem, we proved uniqueness locally for specifically suitable exponents. Furthermore, we established a result for local existence without guaranteeing uniqueness, stating a contraction lemma.

Słowa kluczowe

EN

viscoelastic equation; dispersive term; logarithmic nonlinearity; local existence

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2024
• Tom: Vol. 44, no. 1
• Strony: 19--47
• Opis fizyczny: Bibliogr. 28 poz.

Twórcy

autor

Cordeiro Sebastião

• Federal University of Pará, Faculty of Exact Sciences and Technology, R. Manoel de Abreu, Abaetetuba, 68440–000, Pará, Brazil

• https://orcid.org/0000-0001-5354-2071

autor

Raposo Carlos

• Federal University of Bahia, Department of Mathematics, Av. Milton Santos, Salvador, 40170–110, Bahia, Brazil

• https://orcid.org/0000-0001-8014-7499

autor

Ferreira Jorge

• Federal Fluminense University, Department of Exact Sciences, Avenida dos Trabalhadores, Volta Redonda, 27255–125, Rio de Janeiro, Brazil

• https://orcid.org/0000-0002-3209-7439

autor

Rocha Daniel

• Federal University of Pará, Institute of Exact and Natural Sciences, R. Augusto Corrêa, Belém, 66075–110, Pará, Brazil

• https://orcid.org/0000-0002-3115-354X

autor

Shahrouzi Mohammad

• Jahrom University, Department of Mathematics, GJPJ+8PW, Jahrom, 74137–66171, Fars Province, Iran

• https://orcid.org/0000-0001-9308-0115

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)