Initial boundary value problem for p-Laplacian type parabolic equation with singular potential and logarithmic nonlinearity

被引：0
作者：
Wen-Shuo Yuan
Bin Ge
Qing-Hai Cao
机构：
[1] Harbin Engineering University,School of Mathematical Sciences
来源：
Analysis and Mathematical Physics | 2023年 / 13卷
关键词：
Pseudo parabolic equation; -Laplacian; Logarithmic nonlinearity; Singular potential; Local existence; Global existence; Decay estimate; Blow-up;
D O I：
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学科分类号：
摘要：
The aim of this paper is to utilize special skills and potential well method to deal with questions of local and global well-posedness to a nonlinear diffusion equation driven by the p-Laplace operator, which reveals a subtle relationship between singular potential and nonlinear operator, and further generalizes some previous early results about local existence of the weak solution from a class of evolution equations involved the linear dissipative term and singular potential. Specifically, the results of stability and blow-up of solutions are established for the first time to this initial boundary value problem with singular potential.
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  • [1] Chen PJ(1968)On a theory of heat conduction involving two temperatures Z. Angew. Math. Phys. 19 614-627
  • [2] Gurtin ME(1976)Nonlinear wave mechanics Ann. Phys. 100 62-93
  • [3] Bialynicki-Burula I(2013)Global existence of weak solutions for a logarithmic wave equation arising from Q-balldynamics Bull. Korean Math. Soc. 50 275-283
  • [4] Mycielski J(2019)Polynomial decay rate for Kirchhoff type in viscoelasticity with logarithmic nonlinearity and not necessarily decreasing kernel Symmetry 11 1-24
  • [5] Han XS(2009)Logarithmic Klein–Gordon equation Acta Phys. Pol. B 40 59-66
  • [6] Boulaaras S(2006)Smooth attractors for strongly damped wave equations Nonlinearity 19 1495-1506
  • [7] Draifia A(2015)Initial boundary value problem for a class of semilinear pseudo-parabolic equations with logarithmic nonlinearity J. Differ. Equ. 258 4424-4442
  • [8] Alnegga M(2022)Lifespan of solutions to a damped plate equation with logarithmic nonlinearity Evol. Equ. Control Theory 11 25-40
  • [9] Górka P(2020)Global well-posedness of nonlinear wave equation with weak and strong damping terms and logarithmic source term Adv. Nonlinear Anal. 9 613-632
  • [10] Vittorino P(2018)Energy decay estimates and infinite blow-up phenomena for a strongly damped semilinear wave equation with logarithmic nonlinear source Math. Methods Appl. Sci. 41 2639-2653
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