Nonlinear Elliptic Equations with Singular Boundary Conditions

Zhang, Zhijun

doi:10.1006/jmaa.1997.5635

Cited by 17 publications

(7 citation statements)

References 11 publications

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“…The proof is motivated by the appendix in [11]. Choose Q i,T = Ω i × (0, T ] (i = 1, 2, 3), where Ω Ω 1 Ω 2 Ω 3 Ω having smooth boundaries.…”

Section: The Main Results and The Proofsmentioning

confidence: 99%

Existence, uniqueness and asymptotic behavior of solutions for a singular parabolic equation

Yao

2009

Journal of Mathematical Analysis and Applications

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In this paper, we are concerned with a singular parabolic equationin a smooth bounded domain Ω ⊂ R N subject to zero Dirichlet boundary condition and initial condition ϕ 0. Under the assumptions on μ, ϕ and f (x, t), some existence and uniqueness results are obtained by applying parabolic regularization method and the subsupersolutions method. We also discuss the asymptotic behaviors of solutions in the sense of L 2 (0, T ; W 1,2 0 (Ω)) and L ∞ (0, T ; L 2 (Ω)) norms as μ → 0 or μ → ∞. As a byproduct we obtain the existence of solutions for some problems which blow up on the boundary.

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“…The proof is motivated by the appendix in [11]. Choose Q i,T = Ω i × (0, T ] (i = 1, 2, 3), where Ω Ω 1 Ω 2 Ω 3 Ω having smooth boundaries.…”

Section: The Main Results and The Proofsmentioning

confidence: 99%

Existence, uniqueness and asymptotic behavior of solutions for a singular parabolic equation

Yao

2009

Journal of Mathematical Analysis and Applications

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“…Lasry and Lions [25] established existence, uniqueness and exact asymptotical behaviour of solutions near the boundary to problem (P − ) for g(u) = λu with λ > 0 and q > 1. For other existence results of large solutions to elliptic problems with nonlinear gradient terms, see [41,45].…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

Boundary blow-up elliptic problems with nonlinear gradient terms

Zhang

2006

Journal of Differential Equations

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By Karamata regular variation theory and perturbation method, we show the exact asymptotical behaviour of solutions near the boundary to nonlinear elliptic problems u ± |∇u| q = b(x)g(u), u > 0 in Ω, u| ∂Ω = +∞, where Ω is a bounded domain with smooth boundary in R N , q 0, g ∈ C 1 [0, ∞), g(0) = 0, g is regularly varying at infinity with index ρ with ρ > 0 and b is nonnegative nontrivial in Ω, which may be vanishing on the boundary.

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“…For other existence results of large solutions to elliptic problems with nonlinear gradient terms, see [44,48,50] and the references therein.…”

Section: Z Zhangmentioning

confidence: 99%

Boundary blow-up elliptic problems with nonlinear gradient terms and singular weights

Zhang¹

2008

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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By Karamata regular variation theory, a perturbation method and construction of comparison functions, we show the exact asymptotic behaviour of solutions near the boundary to nonlinear elliptic problems ∆uwhere Ω is a bounded domain with smooth boundary in R N , q > 0, g ∈ C 1 [0, ∞) is increasing on [0, ∞), g(0) = 0, g is regularly varying at infinity with positive index ρ and b is non-negative in Ω and is singular on the boundary.

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Nonlinear Elliptic Equations with Singular Boundary Conditions

Cited by 17 publications

References 11 publications

Existence, uniqueness and asymptotic behavior of solutions for a singular parabolic equation

Existence, uniqueness and asymptotic behavior of solutions for a singular parabolic equation

Boundary blow-up elliptic problems with nonlinear gradient terms

Boundary blow-up elliptic problems with nonlinear gradient terms and singular weights

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