Nonexistence of global solutions for a nonlinear parabolic equation with a forcing term

• Autorzy: Alshehri Aisha , Aljaber Noha , Altamimi Haya , Alessa Rasha , Majdoub Mohamed

Identyfikatory

DOI

10.7494/OpMath.2023.43.6.741

• Języki publikacji: EN

Abstrakty

EN

The purpose of this work is to analyze the blow-up of solutions of a nonlinear parabolic equation with a forcing term depending on both time and space variables ut − Δu = |x|α|u|p + a(t)w(x) for (t, x) ∈ (0,∞) × RN, where α ∈ R, p > 1, and a(t) as well as w(x) are suitable given functions. We generalize and somehow improve earlier existing works by considering a wide class of forcing terms that includes the most common investigated example tσ w(x) as a particular case. Using the test function method and some differential inequalities, we obtain sufficient criteria for the nonexistence of global weak solutions. This criterion mainly depends on the value of the limit lim [formula]. The main novelty lies in our treatment of the nonstandard condition on the forcing term.

Słowa kluczowe

EN

nonlinear heat equation; forcing term; blow-up; test function; differential inequalities

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2023
• Tom: Vol. 43, no. 6
• Strony: 741--758
• Opis fizyczny: Bibliogr. 34 poz.

Twórcy

autor

Alshehri Aisha

• Department of Mathematics, College of Science, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam, Saudi Arabia
• Basic and Applied Scientific Research Center, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, 31441, Dammam, Saudi Arabia

autor

Aljaber Noha

• Department of Mathematics, College of Science, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam, Saudi Arabia
• Basic and Applied Scientific Research Center, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, 31441, Dammam, Saudi Arabia

autor

Altamimi Haya

• Department of Mathematics, College of Science, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam, Saudi Arabia
• Basic and Applied Scientific Research Center, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, 31441, Dammam, Saudi Arabia

autor

Alessa Rasha

• Department of Mathematics, College of Science, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam, Saudi Arabia
• Basic and Applied Scientific Research Center, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, 31441, Dammam, Saudi Arabia

autor

Majdoub Mohamed

• Department of Mathematics, College of Science, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam, Saudi Arabia
• Basic and Applied Scientific Research Center, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, 31441, Dammam, Saudi Arabia

• https://orcid.org/0000-0001-6038-1069

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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)