Well‐posedness and stability for a Petrovsky equation with properties of nonlinear localized for strong damping

2020 ◽  
Author(s):  
Hocine Mohamed Braiki ◽  
Mama Abdelli ◽  
Sabeur Mansouri ◽  
Khaled Zennir
Keyword(s):  
Well Posedness ◽  
Strong Damping ◽  
Petrovsky Equation

scholarly journals Well-posedness and general energy decay of solutions for a Petrovsky equation with a nonlinear strong dissipation

Mathematica ◽  
2021 ◽  
Vol 63 (86) (2) ◽  
pp. 284-296
Author(s):  
Tayeb Lakroumbe ◽  
◽  
Mama Abdelli ◽  
Naima Louhibi ◽  
Mounir Bahlil ◽  
...  
Keyword(s):  
Asymptotic Behaviour ◽  
Bounded Domain ◽  
Energy Method ◽  
Energy Decay ◽  
Well Posedness ◽  
Galerkin Procedure ◽  
Decay Of Solutions ◽  
General Energy ◽  
Uniqueness Of The Solution ◽  
Petrovsky Equation

We consider a nonlinear Petrovsky equation in a bounded domain with a strong dissipation, and prove the existence and the uniqueness of the solution using the energy method combined with the Faedo-Galerkin procedure under certain assumptions. Furthermore, we study the asymptotic behaviour of the solutions using a perturbed energy method.

Well posedness and exponential stability in a wave equation with a strong damping and a strong delay

2016 ◽  
Vol 57 (11) ◽  
pp. 111501 ◽  
Author(s):  
Salim A. Messaoudi ◽  
Abdelfeteh Fareh ◽  
Nadjet Doudi
Keyword(s):  
Wave Equation ◽  
Exponential Stability ◽  
Well Posedness ◽  
Strong Damping

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

scholarly journals The BV solution of the parabolic equation with degeneracy on the boundary

2016 ◽  
Vol 14 (1) ◽  
pp. 272-282
Author(s):  
Huashui Zhan ◽  
Shuping Chen
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Well Posedness ◽  
Test Functions ◽  
The Stability

AbstractConsider a parabolic equation which is degenerate on the boundary. By the degeneracy, to assure the well-posedness of the solutions, only a partial boundary condition is generally necessary. When 1 ≤ α < p – 1, the existence of the local BV solution is proved. By choosing some kinds of test functions, the stability of the solutions based on a partial boundary condition is established.

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