Problem of determining the nonstationary potential in a hyperbolic-type equation

2008 ◽  
Vol 156 (2) ◽  
pp. 1154-1158 ◽  
Author(s):  
D. K. Durdiev
Keyword(s):  
Type Equation ◽  
Hyperbolic Type ◽  
Nonstationary Potential

scholarly journals Find A General Solution Of An Equation Of The Hyperbolic Type With A Second-Order Singular Coefficient And Solve The Cauchy Problem Posed For This Equation.

2021 ◽  
Vol 25 (1) ◽  
pp. 80
Author(s):  
Karimova Shalola Musayevna ◽  
Melikuzieva Dilshoda Mukhtorjon qizi
Keyword(s):  
Cauchy Problem ◽  
General Solution ◽  
Type Equation ◽  
Second Order ◽  
Hyperbolic Type ◽  
Singular Coefficient ◽  
The Cauchy Problem

This paper presents a general solution of a hyperbolic type equation with a second-order singular coefficient and a solution to the Cauchy problem posed for this equation.

scholarly journals Inverse source problems for time-fractional mixed parabolic-hyperbolic-type equations

2015 ◽  
Vol 23 (4) ◽  
Author(s):  
Pengbin Feng ◽  
Erkinjon T. Karimov
Keyword(s):  
Wave Equation ◽  
Mixed Type ◽  
Orthonormal System ◽  
Type Equation ◽  
Hyperbolic Type ◽  
Initial Time ◽  
Inverse Source Problem ◽  
Ill Posed ◽  
Inverse Source Problems ◽  
Well Posed

AbstractIn the present paper we consider an inverse source problem for a time-fractional mixed parabolic-hyperbolic equation with Caputo derivatives. In the case when the hyperbolic part of the considered mixed-type equation is the wave equation, the uniqueness of the source and the solution are strongly influenced by the initial time and the problem is generally ill-posed. However, when the hyperbolic part is time-fractional, the problem is well-posed if the end time is large. Our method relies on the orthonormal system of eigenfunctions of the operator with respect to the space variables. Finally, we prove uniqueness and stability of certain weak solutions for the problems under consideration.

scholarly journals Solvability of BVPs for the Parabolic-Hyperbolic Equation with Non-linear Loaded Term

2021 ◽  
pp. 133-145
Author(s):  
Obidjon Kh. Abdullaev
Keyword(s):  
Hyperbolic Equation ◽  
Existence And Uniqueness ◽  
Type Equation ◽  
Existence Of Solution ◽  
Hyperbolic Type ◽  
Uniqueness Of Solution ◽  
Method Of Integral Equations ◽  
Non Local ◽  
Integral Energy ◽  
Loaded Term

This work is devoted to prove the existence and uniqueness of solution of BVP with non-local assumptions on the boundary and integral gluing conditions for the parabolic-hyperbolic type equation involving Caputo derivatives. Using the method of integral energy, the uniqueness of solution have been proved. Existence of solution was proved by the method of integral equations

Integral Operators that Determine the Solution of an Iterated Hyperbolic-Type Equation

2020 ◽  
Vol 56 (3) ◽  
pp. 401-409
Author(s):  
I. M. Alexandrovich ◽  
O. S. Bondar ◽  
S. I. Lyashko ◽  
N. I. Lyashko ◽  
M. V.-S. Sydorov
Keyword(s):  
Integral Operators ◽  
Type Equation ◽  
Hyperbolic Type
Sign in / Sign up

Export Citation Format

Share Document