Integral type Cauchy problem for abstract wave equations and applications

2021 ◽  
pp. 1-26
Author(s):  
Ravi P. Agarwal ◽  
Veli B. Shakhmurov
Keyword(s):  
Cauchy Problem ◽  
Wave Equations ◽  
Integral Type

Hyperbolic Mixed Problems for Harmonic Tensors

1957 ◽  
Vol 9 ◽  
pp. 161-179 ◽  
Author(s):  
G. F. D. Duff
Keyword(s):  
Boundary Condition ◽  
Cauchy Problem ◽  
Principal Part ◽  
Wave Equations ◽  
Initial Conditions ◽  
Boundary Surface ◽  
Cauchy Data ◽  
Riemann Space ◽  
Initial Value ◽  
Mixed Problems

This paper may be regarded as a sequel to (1), where the initial value or Cauchy problem for harmonic tensors on a normal hyperbolic Riemann space was treated. The mixed problems to be studied here involve boundary conditions on a timelike boundary surface in addition to the Cauchy data on a spacelike initial manifold. The components of a harmonic tensor satisfy a system of wave equations with similar principal part, and we assign two initial conditions and one boundary condition for each component.

On the convergence of the method of finite differences applied to the solution of the initial value problem for functional-differential neutral type equations

1981 ◽  
Vol 89 (3-4) ◽  
pp. 259-265
Author(s):  
N. G. Kazakova ◽  
D. D. Bainov
Keyword(s):  
Cauchy Problem ◽  
Initial Value Problem ◽  
Finite Differences ◽  
Neutral Type ◽  
Integral Type ◽  
Initial Value ◽  
Natural Class ◽  
Quadrature Formulae ◽  
The Cauchy Problem ◽  
Functional Differential

SynopsisWhen solving practically the neutral type equations the derivatives are replaced by finite differences while the members of integral type are replaced by quadrature formulae. The paper deals with the convergence of a natural class of methods applied to the Cauchy problem for functional-differential neutral type equations. It is not obligatory for the approximated operators to be compact.

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