Existence and Uniqueness of Weak and Classical Solutions for a Fourth-Order Semilinear Boundary Value Problem

Danet, Cristian-Paul

doi:10.1017/s1446181119000129

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2022

2023

Publication Types

Select...

Other1

Article1

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(1 citation statement)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Fourth order PDEs have several applications, for example, in elastic beam deformations [5,6], in thin plate theory [7,8] and in image processing [9]. The p-biharmonic problems are at the intersection of these fields of study.…”

Section: Introductionmentioning

confidence: 99%

Mixed finite element method for a beam equation with the p-biharmonic operator

Almeida¹,

Duque²,

Ferreira³

et al. 2022

Preprint

View full text Add to dashboard Cite

In this paper, we consider a nonlinear beam equation with the p-biharmonic operator, where 1 < p < ∞. Using a change of variable, we transform the problem into a system of differential equations and prove the existence, uniqueness and regularity of the weak solution by applying the Lax-Milgram theorem and classical results of functional analysis. We investigate the discrete formulation for that system and, with the aid of the Brouwer theorem, we show that the problem has a discrete solution. The uniqueness and stability of the discrete solution are obtained through classical methods. After establishing the order of convergence, we apply the mixed finite element method to obtain an algebraic system of equations. Finally, we implement the computational codes in Matlab software and perform the comparison between theory and simulations.

show abstract