scholarly journals Global existence for the one-dimensional second order semilinear hyperbolic equations

2008 ◽  
Vol 344 (1) ◽  
pp. 76-98 ◽  
Author(s):  
Anahit Galstian
Keyword(s):  
Global Existence ◽  
Hyperbolic Equations ◽  
Second Order ◽  
One Dimensional ◽  
The One

scholarly journals Preserving the Shape of Functions by Applying Multidimensional Schoenberg-Type Operators

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1016
Author(s):  
Camelia Liliana Moldovan ◽  
Radu Păltănea
Keyword(s):  
Applied Sciences ◽  
Degree Of Approximation ◽  
Higher Order ◽  
Second Order ◽  
Dimensional Case ◽  
Moduli Of Continuity ◽  
One Dimensional ◽  
Multidimensional Generalization ◽  
The One

The paper presents a multidimensional generalization of the Schoenberg operators of higher order. The new operators are powerful tools that can be used for approximation processes in many fields of applied sciences. The construction of these operators uses a symmetry regarding the domain of definition. The degree of approximation by sequences of such operators is given in terms of the first and the second order moduli of continuity. Extending certain results obtained by Marsden in the one-dimensional case, the property of preservation of monotonicity and convexity is proved.

The problem of determining the one-dimensional kernel of viscoelasticity equation with a source of explosive type

2020 ◽  
Vol 28 (1) ◽  
pp. 43-52
Author(s):  
Durdimurod Kalandarovich Durdiev ◽  
Zhanna Dmitrievna Totieva
Keyword(s):  
Inverse Problem ◽  
Hyperbolic Equations ◽  
Stability Estimate ◽  
Continuous Functions ◽  
System Of Integral Equations ◽  
One Dimensional ◽  
Weighted Norms ◽  
The Stability ◽  
The One ◽  
Global Unique Solvability

AbstractThe integro-differential system of viscoelasticity equations with a source of explosive type is considered. It is assumed that the coefficients of the equations depend only on one spatial variable. The problem of determining the kernel included in the integral terms of the equations is studied. The solution of the problem is reduced to one inverse problem for scalar hyperbolic equations. This inverse problem is replaced by an equivalent system of integral equations for unknown functions. The principle of constricted mapping in the space of continuous functions with weighted norms to the latter is applied. The theorem of global unique solvability is proved and the stability estimate of solution to the inverse problem is obtained.

scholarly journals CABARET FINITE‐DIFFERENCE SCHEMES FOR THE ONE‐DIMENSIONAL EULER EQUATIONS

2001 ◽  
Vol 6 (2) ◽  
pp. 210-220 ◽  
Author(s):  
V. M. Goloviznin ◽  
T. P. Hynes ◽  
S. A. Karabasov
Keyword(s):  
Time Derivative ◽  
Second Order ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Gas Flows ◽  
Time Layer ◽  
One Dimensional ◽  
Upwind Schemes ◽  
The One ◽  
Solution Accuracy

In the present paper we consider second order compact upwind schemes with a space split time derivative (CABARET) applied to one‐dimensional compressible gas flows. As opposed to the conventional approach associated with incorporating adjacent space cells we use information from adjacent time layer to improve the solution accuracy. Taking the first order Roe scheme as the basis we develop a few higher (i.e. second within regions of smooth solutions) order accurate difference schemes. One of them (CABARET3) is formulated in a two‐time‐layer form, which makes it most simple and robust. Supersonic and subsonic shock‐tube tests are used to compare the new schemes with several well‐known second‐order TVD schemes. In particular, it is shown that CABARET3 is notably more accurate than the standard second‐order Roe scheme with MUSCL flux splitting.

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