Regularity and existence of solutions to parabolic equations with nonstandard p(x,t),q(x,t)-growth conditions

• Autorzy: El Bahja Hamid

Identyfikatory

DOI

10.7494/OpMath.2023.43.6.759

• Języki publikacji: EN

Abstrakty

EN

We study the Cauchy–Dirichlet problem for a class of nonlinear parabolic equations driven by nonstandard p(x, t), q(x, t)-growth condition. We prove theorems of existence and uniqueness of weak solutions in suitable Orlicz-Sobolev spaces, derive global and local in time L∞ bounds for the weak solutions.

Słowa kluczowe

EN

existence theory; non-linear parabolic problems; non-standard growth; regularity theory

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2023
• Tom: Vol. 43, no. 6
• Strony: 759--788
• Opis fizyczny: Bibliogr. 25 poz.

Twórcy

autor

El Bahja Hamid

• African Institute for Mathematical Sciences, Cape Town, South Africa

• https://orcid.org/0000-0002-0945-2105

Bibliografia

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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)