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  1. On One Cauchy Problem for a Hyperbolic Differential-Difference Equation

    Abstract

    We provide a formulation of the Cauchy problem in a strip for a two-dimensional hyperbolic equation containing a superposition of a...

    N. V. Zaitseva in Differential Equations
    Article 01 December 2023

  3. Hyperbolic Theory

    This chapter is an introduction to the theory of hyperbolic structures in differential equations. The basic idea that is discussed might be called...
    Carmen Chicone in Ordinary Differential Equations with Applications
    Chapter 2024

  4. Inverse Problem of Determining Two Coefficients of Lower-Order Terms in a Mixed Parabolic-Hyperbolic Equation

    Abstract

    Direct and inverse problems for a model equation of mixed parabolic-hyperbolic type are studied. In the direct problem, we consider a...

    D. K. Durdiev in Differential Equations
    Article 01 January 2024

  5. On a Problem for a Parabolic-Hyperbolic Equation with a Nonlinear Loaded Part

    The existence and uniqueness theorems of the solution to the boundary-value problem for a parabolic-hyperbolic fractional-order equation with the...

    O. Kh. Abdullaev in Journal of Mathematical Sciences
    Article 11 October 2023

  6. On an Inverse Problem for the Hyperbolic Equation

    The paper considers the inverse problem of determining the unknown coefficient on the righthand side of the hyperbolic equation. An additional...

    Adalat Ya. Akhundov, Arasta Sh. Habibova in Journal of Mathematical Sciences
    Article 19 November 2022

  7. Inverse Problems for the Loaded Parabolic-Hyperbolic Equation Involves Riemann–Liouville Operator

    Abstract

    In this article, the existence and the uniqueness of solution of inverse problems with non-linear gluing condition for the loaded...

    O. Kh. Abdullaev, T. K. Yuldashev in Lobachevskii Journal of Mathematics
    Article 01 March 2023

  8. Mean-Value Formula for a Hyperbolic Equation with a Factorizable Operator

    A mean-value formula for a linear partial differential hyperbolic equation with an operator splitting into first-order factors is obtained. This...

    M. V. Polovinkina in Journal of Mathematical Sciences
    Article 17 November 2022

  9. Inverse Problem for a Third-Order Parabolic-Hyperbolic Equation Involves Fractional Derivatives

    Abstract

    In this article the questions of unique solvability of inverse problem for a third order parabolic-hyperbolic type equation with Caputo...

    A. A. Matchanova in Lobachevskii Journal of Mathematics
    Article 01 March 2023

  10. Inverse Problem for a Non-Homogeneous Integro-Differential Equation of the Hyperbolic Type

    Abstract

    The inverse problem of determining the solution and one-dimensional kernel of the integral term in an inhomogeneous integro-differential...

    J. Sh. Safarov in Vestnik St. Petersburg University, Mathematics
    Article 01 March 2024

  11. Tricomi Problem for Mixed Parabolic–Hyperbolic Equation with Higher Order Boundary Condition

    In this paper, we study an analogue of Tricomi problem for a parabolic–hyperbolic equation. One boundary condition in the parabolic part of the...

    Bauyrzhan Derbissaly, Makhmud Sadybekov in Bulletin of the Iranian Mathematical Society
    Article 30 June 2023

  12. Determining the Coefficient of a Mixed Parabolic-Hyperbolic Equation with Noncharacteristic Type Change Line

    Abstract

    Direct and inverse problems for a model equation of the mixed parabolic-hyperbolic type are studied. The direct problem is an analog of the...

    D. K. Durdiev in Differential Equations
    Article 01 December 2022

  13. The Global Classical Solution and Asymptotic Behavior of the Cauchy Problem for Hyperbolic Monge-Ampère Equation

    This paper is concerned with the hyperbolic partial differential equations of Monge-Ampère type with two independent variables. When the coefficients...

    Qinfeng Jiang, Changhua Wei, Tiantian **ng in Results in Mathematics
    Article 10 November 2023

  14. Classical Solution to the Cauchy Problem for a Semilinear Hyperbolic Equation in the Case of Two Independent Variables

    Abstract

    In the upper half-plane, we consider a semilinear hyperbolic partial differential equation of order higher than two. The operator in the...

    V. I. Korzyuk, J. V. Rudzko in Russian Mathematics
    Article 01 March 2024

  15. A numerical technique based on Legendre wavelet for linear and nonlinear hyperbolic telegraph equation

    This study is devoted to the numerical investigation of linear and nonlinear hyperbolic telegraph equation. We have proposed a wavelet collocation...

    Basharat Hussain, Mo Faheem, Arshad Khan in Journal of Applied Mathematics and Computing
    Article 10 May 2024

  16. Coefficient Inverse Problem for an Equation of Mixed Parabolic-Hyperbolic Type with a Noncharacteristic Line of Type Change

    Abstract

    In this paper, the direct and two inverse problems for a model equation of mixed parabolic-hyperbolic type are studied. In the direct...

    D. K. Durdiev in Russian Mathematics
    Article 01 March 2024

  17. Analytical Solution of One Non-Local Problem for Hyperbolic Equation

    Abstract

    In this paper we consider small oscillations of the ideal gas near its equilibrium state inside an unbounded cylindrical tube. We investigate...

    V. B. Vasilyev, N. V. Zaitseva in Lobachevskii Journal of Mathematics
    Article 01 July 2023

  18. Family of Smooth Solutions of Hyperbolic Differential-Difference Equation

    Three-parameter familie of solutions is constructed for hyperbolic differential-difference equation with shift operators of the general-type acting...
    Natalya V. Zaitseva in Differential Equations, Mathematical Modeling and Computational Algorithms
    Conference paper 2023

  19. Local Boundary Value Problems for a Degenerate Loaded Equation of Parabolic-Hyperbolic Type of the Second Kind

    Abstract

    In the present paper, we pose and study local boundary value problems for a parabolic-hyperbolic equation of the second kind with...

    B. I. Islomov, D. A. Nasirova in Lobachevskii Journal of Mathematics
    Article 01 December 2023

  20. Solvability of One-Dimensional Semilinear Hyperbolic Systems and Sine-Gordon Equation

    We study semilinear hyperbolic Eq. ( 1.1 ). We derive an explicit solution representation for some nonlinear terms F and G . For other nonlinear terms,...

    Hyung** Huh in Journal of Nonlinear Mathematical Physics
    Article Open access 07 July 2023
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