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- W4323923525 abstract "We study the Dirichlet problem for the pseudo-parabolic equationut=div(|∇u|p(x,t)−2∇u)+Δut+f(x,t,u,∇u) in the cylinder (x,t)∈QT=Ω×(0,T), Ω⊂Rd, d≥2. It is shown that under appropriate conditions on the regularity of the data and the growth of the source f with respect to the second and third arguments, the problem has a global in time solution with the propertiesu∈L∞(0,T;H02(Ω)),ut,|∇ut|∈L2(QT),|∇u|∈L∞(0,T;Lp(⋅)(Ω))∩Lp(⋅,⋅)+δ(QT) with some δ>0. For special choices of the source f, sufficient conditions of uniqueness are derived, stability of solutions with respect to perturbations of the nonlinear structure of the equation is proven, and the rate of vanishing of ‖u‖W1,2(Ω) is found." @default.
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- W4323923525 date "2023-10-01" @default.
- W4323923525 modified "2023-10-06" @default.
- W4323923525 title "Global existence and regularity for a pseudo-parabolic equation with p(x,t)-Laplacian" @default.
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- W4323923525 doi "https://doi.org/10.1016/j.jmaa.2023.127202" @default.
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