Nonlinear elliptic–parabolic problem involving p-Dirichlet-to-Neumann operator with critical exponent

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Abstract: We consider the nonlinear elliptic–parabolic boundary value problem involving the Dirichlet-to-Neumann operator of p-Laplace type at the critical Sobolev exponent. We first obtain the existence and asymptotic estimates of the global solution, and the sufficient conditions of finite time blowup of the solution by using the energy method. Second, we improve the regularity of solution by Moser-type iteration. Finally, we analyze the long-time asymptotic behavior of the global solution. Moreover, with the help of the concentration compactness principle, we present a precise description of the concentration phenomenon of the solution in the forward time infinity.

Location
Deutsche Nationalbibliothek Frankfurt am Main
Extent
Online-Ressource
Language
Englisch

Bibliographic citation
Nonlinear elliptic–parabolic problem involving p-Dirichlet-to-Neumann operator with critical exponent ; volume:12 ; number:1 ; year:2023 ; extent:23
Advances in nonlinear analysis ; 12, Heft 1 (2023) (gesamt 23)

Creator
Deng, Yanhua
Tan, Zhong
Xie, Minghong

DOI
10.1515/anona-2022-0306
URN
urn:nbn:de:101:1-2023032814192706024468
Rights
Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
Last update
14.08.2025, 10:54 AM CEST

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Associated

  • Deng, Yanhua
  • Tan, Zhong
  • Xie, Minghong

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