scholarly journals Existence of solutions for quasilinear problem with Neumann boundary conditions

2022 ◽  
Vol 40 ◽  
pp. 1-8
Author(s):  
Samira Lecheheb ◽  
Hakim Lakhal ◽  
Messaoud Maouni
Keyword(s):  
Boundary Conditions ◽  
Heat Equation ◽  
Existence Of Solutions ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Compactness Method ◽  
Quasilinear Systems ◽  
Quasilinear Problem

My abstract is:This paper is devoted to the study of the existence of weak solutionsfor quasilinear systems of a partial dierential equations which are the combinationof the Perona-Malik equation and the Heat equation. The proof of the main resultsare based on the compactness method and the motonocity arguments.

scholarly journals Analytical Solution of Homogeneous One-Dimensional Heat Equation with Neumann Boundary Conditions

2020 ◽  
Vol 1551 ◽  
pp. 012002
Author(s):  
Norazlina Subani ◽  
Faizzuddin Jamaluddin ◽  
Muhammad Arif Hannan Mohamed ◽  
Ahmad Danial Hidayatullah Badrolhisam
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Heat Equation ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
One Dimensional

scholarly journals Existence of solutions for a fourth order eigenvalue problem with variable exponent under Neumann boundary conditions

2016 ◽  
Vol 34 (1) ◽  
pp. 253-272
Author(s):  
Khalil Ben Haddouch ◽  
Zakaria El Allali ◽  
Najib Tsouli ◽  
Siham El Habib ◽  
Fouad Kissi
Keyword(s):  
Boundary Conditions ◽  
Fourth Order ◽  
Variable Exponent ◽  
Existence Of Solutions ◽  
Neumann Boundary ◽  
Growth Conditions ◽  
Neumann Boundary Conditions ◽  
Order Elliptic Equation ◽  
Fourth Order Eigenvalue Problem ◽  
Fourth Order Elliptic Equation

In this work we will study the eigenvalues for a fourth order elliptic equation with $p(x)$-growth conditions $\Delta^2_{p(x)} u=\lambda |u|^{p(x)-2} u$, under Neumann boundary conditions, where $p(x)$ is a continuous function defined on the bounded domain with $p(x)>1$. Through the Ljusternik-Schnireleman theory on $C^1$-manifold, we prove the existence of infinitely many eigenvalue sequences and $\sup \Lambda =+\infty$, where $\Lambda$ is the set of all eigenvalues.

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