scholarly journals THE WELL-POSEDNESS OF THE MIXED PROBLEM FOR ONE SYSTEM OF THERMOELASTICITY WITH A SINGULAR COEFFICIENT

2021 ◽  
pp. 301-308
Keyword(s):  
Mixed Problem ◽  
Well Posedness ◽  
Singular Coefficient

scholarly journals THE WELL-POSEDNESS OF MIXED PROBLEM FOR ONE CLASS OF DEGENERATE MULTI-DIMENSIONAL HYPERBOLIC EQUATIONS

2019 ◽  
pp. 5-14
Author(s):  
S. A. Aldashev
Keyword(s):  
Boundary Value Problems ◽  
Classical Solution ◽  
Explicit Form ◽  
Mixed Problem ◽  
Unique Solvability ◽  
Hyperbolic Equations ◽  
Boundary Value ◽  
Well Posedness ◽  
Elastic Membranes ◽  
Explicit Representations

Oscillations of elastic membranes in 3D are modelled as degenerate multi-dimensional hyperbolic equations. For applied work, it is important to obtain explicit representations of solution of the studied boundary-value problems. This paper shows the unique solvability and obtains the explicit form of the classical solution of the mixed problem for degenerate multi-dimensional hyperbolic equations.

On Solutions of a Singular Viscoelastic Equation with an Integral Condition

2009 ◽  
Vol 16 (4) ◽  
pp. 761-778
Author(s):  
Hacene Mecheri ◽  
Said Mesloub ◽  
Salim A. Messaoudi
Keyword(s):  
Functional Analysis ◽  
Mixed Problem ◽  
A Priori ◽  
Integral Condition ◽  
Analysis Approach ◽  
Well Posedness ◽  
A Priori Bounds ◽  
Viscoelastic Equation

Abstract In this work, we use a functional analysis approach to prove the well posedness of a mixed problem with a nonclassical condition for a viscoelastic equation with dissipation. The proof is mainly based on some a priori bounds and on some density arguments.

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