On a parabolic equation related to the p-Laplacian

Zhan, Huashui

doi:10.1186/s13661-016-0587-6

Cited by 14 publications

(15 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Here, , Ω is a bounded domain in with appropriately smooth boundary, and at least there is a such that . Zhan [2] had shown that the stability of the solutions to the equation is true, where is distance function, is a constant. The result of [2] is in complete antithesis to that of [1].…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

See 1 more Smart Citation

On the evolutionary p-Laplacian equation with a partial boundary value condition

Zhan¹

2018

J Inequal Appl

Self Cite

View full text Add to dashboard Cite

Consider the equation where Ω is a bounded domain, is the distance function from the boundary ∂Ω. Since the nonlinearity, the boundary value condition cannot be portrayed by the Fichera function. If , a partial boundary value condition is portrayed by a new way, the stability of the weak solutions is proved by this partial boundary value condition. If , the stability of the weak solutions may be proved independent of the boundary value condition.

show abstract

Section: Introduction and The Main Resultsmentioning

confidence: 99%

“…Zhan [2] had shown that the stability of the solutions to the equation is true, where is distance function, is a constant. The result of [2] is in complete antithesis to that of [1]. So, when the well-posedness of the solutions is considered, the degeneracy of the diffusion coefficient plays an important role.…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

On the evolutionary p-Laplacian equation with a partial boundary value condition

Zhan¹

2018

J Inequal Appl

Self Cite

View full text Add to dashboard Cite

show abstract

“…and shown that condition (8) may act as the role as the boundary value condition (3) and ensure the well-posedness of the solutions [12][13][14][15]. Coming back to (1).…”

Section: Introductionmentioning

confidence: 99%

On the Non-Newtonian Fluid Equation with a Source Term and a Damping Term

Zhan

Li²

2018

Journal of Function Spaces

Self Cite

View full text Add to dashboard Cite

A kind of non-Newtonian fluid equation with a damping term and a source term is considered. After giving a result of the existence, if the diffusion coefficient is degenerate on the boundary, the local stability of the weak solutions is established without any boundary condition. If the diffusion coefficient is degenerate on a part of the boundary, by imposing the homogeneous value condition on the other part of the boundary, the local stability of the weak solutions is proved. Moreover, if the equation is with a damping term, other than the finite propagation property, the results of this paper reveal the essential differences between the non-Newtonian fluid equation and the heat conduction equation in a new way.

show abstract

“…More precisely, we prove the stability of the unique weak solution to the Dirichlet problem (2) in the sense that the solutions are controlled by the initial value completely, cf. [1][2][3]. The motivation of this paper contains several aspects.…”

Section: Introductionmentioning

confidence: 99%

The Stability of Parabolic Problems with Nonstandard p(x, t)-Growth

Erhardt

2017

Mathematics

View full text Add to dashboard Cite

Abstract:In this paper, we study weak solutions to the following nonlinear parabolic partial differential equation ∂ t u − div a(x, t, ∇u) + λ(|u| p(x,t)−2 u) = 0 in Ω T , where λ ≥ 0 and ∂ t u denote the partial derivative of u with respect to the time variable t, while ∇u denotes the one with respect to the space variable x. Moreover, the vector-field a(x, t, ·) satisfies certain nonstandard p(x, t)-growth and monotonicity conditions. In this manuscript, we establish the existence of a unique weak solution to the corresponding Dirichlet problem. Furthermore, we prove the stability of this solution, i.e., we show that two weak solutions with different initial values are controlled by these initial values.

show abstract

On a parabolic equation related to the p-Laplacian

Cited by 14 publications

References 10 publications

On the evolutionary p-Laplacian equation with a partial boundary value condition

On the evolutionary p-Laplacian equation with a partial boundary value condition

On the Non-Newtonian Fluid Equation with a Source Term and a Damping Term

The Stability of Parabolic Problems with Nonstandard p(x, t)-Growth

Contact Info

Product

Resources

About