Weakened well-posedness of a hyperbolic characteristic boundary value problem

2021 ◽  
Author(s):  
Sihame Brahimi ◽  
Ahmed Zerrouk Mokrane
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Well Posedness ◽  
Characteristic Boundary

The Importance of the Compatibility of Nonlinear Constitutive Theories With Their Linear Counterparts

2006 ◽  
Vol 74 (3) ◽  
pp. 455-460 ◽  
Author(s):  
Ramon Quintanilla ◽  
Giuseppe Saccomandi
Keyword(s):  
Boundary Value Problem ◽  
Mechanical Model ◽  
Linear Viscoelasticity ◽  
Special Class ◽  
Boundary Value ◽  
Well Posedness ◽  
Constitutive Theories ◽  
Nonlinear Viscoelastic ◽  
Simple Boundary ◽  
Nonlinear Viscoelastic Materials

We show, by considering a special class of nonlinear viscoelastic materials, that consistency of a mechanical model with classical linear viscoelasticity, may be a fundamental condition to ensure a mathematical and physical well-posedness behavior. To illustrate our arguments we use a rectilinear class of shear motions that we investigate in the static and quasistatic case in the framework of a simple boundary value problem and the classical recovery phenomenon.

scholarly journals The Periodic Boundary Value Problem for the Weakly Dissipativeμ-Hunter-Saxton Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Zhengyong Ouyang ◽  
Xiangdong Wang ◽  
Haiwu Rong
Keyword(s):  
Boundary Value Problem ◽  
Besov Space ◽  
Periodic Boundary ◽  
Critical Case ◽  
Boundary Value ◽  
Periodic Boundary Value Problem ◽  
Well Posedness

We study the periodic boundary value problem for the weakly dissipativeμ-Hunter-Saxton equation. We establish the local well-posedness in Besov spaceB2,13/2, which extends the previous regularity range to the critical case.

scholarly journals Well-Posedness of the Boundary Value Problem for Parabolic Equations in Difference Analogues of Spaces of Smooth Functions

2007 ◽  
Vol 2007 ◽  
pp. 1-16 ◽  
Author(s):  
A. Ashyralyev
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Approximate Solutions ◽  
Difference Schemes ◽  
Stability Estimates ◽  
Well Posedness ◽  
Nonlocal Boundary Value Problem ◽  
Smooth Functions ◽  
Accuracy Difference

The first and second orders of accuracy difference schemes for the approximate solutions of the nonlocal boundary value problemv′(t)+Av(t)=f(t)(0≤t≤1),v(0)=v(λ)+μ,0<λ≤1, for differential equation in an arbitrary Banach spaceEwith the strongly positive operatorAare considered. The well-posedness of these difference schemes in difference analogues of spaces of smooth functions is established. In applications, the coercive stability estimates for the solutions of difference schemes for the approximate solutions of the nonlocal boundary value problem for parabolic equation are obtained.

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