Well defined extinction time of solutions for a class of weak-viscoelastic parabolic equation with positive initial energy

Himadan, Ahmed

doi:10.3934/math.2021257

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2022

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Cited by 2 publications

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“…Nowadays, problem (1), with p depending on x, is attracting considerable attention, perhaps because of its various physical applications. We refer to [3,26,15], where questions on the solvability and properties of the solutions are addressed.…”

Section: Introductionmentioning

confidence: 99%

A Mixed Finite Element Method for a Class of Evolution Differential Equations with $p$-Laplacian and Memory

Almeida¹,

Duque²,

Mário³

2022

Preprint

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We present a new mixed finite element method for a class of parabolic equations with p-Laplacian and nonlinear memory. The applicability, stability and convergence of the method are studied. First, the problem is written in a mixed formulation as a system of one parabolic equation and a Volterra equation. Then, the system is discretized in the space variable using the finite element method with Lagrangian basis of degree r ≥ 1. Finally, the Cranck-Nicolson method with the trapezoidal quadrature is applied to discretize the time variable. For each method, we establish existence, uniqueness and regularity of the solutions. The convergence order is found to be dependent on the parameter p on the p-Laplacian in the sense that it decreases as p increases.

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Section: Introductionmentioning

confidence: 99%