On the sub-supersolution principle for p(x)-Laplacian equations

Ayazoglu, Rabil; Akbulut, Sezgin; Akkoyunlu, Ebubekir

doi:10.56947/gjom.v6i3.175

Cited by 2 publications

(2 citation statements)

References 13 publications

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“…Beside being of mathematical interest, the study of the p-biharmonic operator is also of interest in micro-electro-mechanical system, in thin film theory, nonlinear surface diffusion on solids, interface dynamics, flow in Hele-Shaw cells, phase field models of multi-phase systems, deformation of a nonlinear elastic beam, (see [8,11,2] and references therein for discussions of various applications).…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Eigenvalues for the p-Biharmonic Dirichlet-Steklov problem with weights

Laghzal

Touzani

2020

GJOM

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Eigenvalues for the p-Biharmonic Dirichlet-Steklov problem with weights

Laghzal

Touzani

2020

GJOM

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“…For investigations into fourth-order degenerate parabolic equations in one spatial dimension, refer to the work in [8]. Given the significance of this topic, recent studies have delved into the existence and uniqueness of differential equations, as evidenced in [3,4,5,16,21,25,27,31,32,33,37].…”

Section: Introductionmentioning

confidence: 99%

Global existence of a pair of coupled Cahn-Hilliard equations with nondegenerate mobility and logarithmic potential

Harfash,

Al-Musawi

2024

GJOM

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We conducted a mathematical investigation on a system of interconnected Cahn-Hilliard equations featuring a logarithmic potential, nondegenerate mobility, and homogeneous Neumann boundary conditions. This system emerges from a model depicting the phase separation of a binary liquid mixture in a thin film. Assuming certain conditions on the initial data, we successfully established the existence, uniqueness, and stability estimates for the weak solution. Our approach involved initially replacing the logarithmic potential with a smooth counterpart, resulting in the regularization of the original problem (Q) into a regularized problem (Qε). Utilizing the Faedo-Galerkin method and compactness arguments, we demonstrated the existence and uniqueness of a solution for (Qε). Subsequently, by letting ε approach zero, we attained the existence of a solution for the original problem (Q). Additionally, we addressed higher regularity aspects of the weak solutions for both (Q) and (Qε). Employing the standard regularity theory for elliptic problems and introducing additional assumptions regarding the domain's boundary and the initial data, we established that the weak solutions belong to higher-order Sobolev spaces.

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On the sub-supersolution principle for p(x)-Laplacian equations

Abstract: This paper deals with the sub-supersolution method for the p(x) -Laplacian Dirichlet problem. A sub-supersolution principle for the Dirichlet problems involving the p(x)-Laplacian is established by using induction method.

Cited by 2 publications

References 13 publications

Eigenvalues for the p-Biharmonic Dirichlet-Steklov problem with weights

Eigenvalues for the p-Biharmonic Dirichlet-Steklov problem with weights

Global existence of a pair of coupled Cahn-Hilliard equations with nondegenerate mobility and logarithmic potential

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