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Three-Dimensional Initial-Boundary Value Problem for a Parabolic-Hyperbolic Equation with a Degenerate Parabolic Part
AbstractAn initial-boundary value problem is studied for a nonhomogeneous equation of mixed parabolic-hyperbolic type in three variables with a...
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The Mixed Initial-Boundary Value Problem for Degenerate Hyperbolic Equation
A new class of initial-boundary value problems with nonlocal conditions on the Newton potential for the case of a degenerate equation were set and...
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The initial-boundary value problem for a strictly hyperbolic equations
This article focuses on constructing the global solutions to initial-boundary value problem for a nonlinear strictly hyperbolic system of...
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Integral Analogue of the First Initial-Boundary Value Problem for Second-Order Hyperbolic and Parabolic Equations
AbstractWe study the solvability of initial-boundary value problems for second-order hyperbolic and parabolic equations with a boundary condition...
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Initial-Boundary Value Problem for a Multidimensional Integro-Differential Equation of Hyperbolic Type and a Difference Method for its Numerical Implementation
AbstractIn this paper, we consider an initial-boundary value problem for a multidimensional integro-differential equation of hyperbolic type. For an...
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Finite Fourier Series in Hyperbolic Initial-Boundary Value Problems for Domains with Curved Boundaries
AbstractThe Fourier method based on orthogonal splines is used to solve a linear hyperbolic initial-boundary value problem for a domain with a curved...
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On the Well-Posedness of an Initial–Boundary Value Problem for a Degenerate Heat Equation
AbstractThe well-posedness of an initial–boundary value problem for a model parabolic equation with two power-law degeneration lines is studied....
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On the initial-boundary value problem for a non-local elliptic-hyperbolic system related to the short pulse equation
In this paper, we prove the well-posedness of the initial-boundary value problem for a non-local elliptic-hyperbolic system related to the short...
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Global classical solutions near vacuum to the initial-boundary value problem of isentropic flows through divergent ducts
In this paper, we study the global existence and asymptotic behavior of classical solutions near vacuum for the initial-boundary value problem...
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Initial–Boundary Value Problem for a Three-Dimensional Equation of the Parabolic-Hyperbolic Type
AbstractWe study an initial–boundary value problem for an equation of the mixed parabolic-hyperbolic type in a rectangular parallelepiped. A...
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On the Solvability of an Initial–Boundary Value Problem for a High Even Order Partial Differential Equation Degenerating on the Domain Boundary
AbstractAn initial–boundary value problem is posed in a rectangle for a degenerate partial differential equation of high even order with a Bessel...
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On a Solution of a Nonlinear Nonlocal Boundary Value Problem for one Class of Hyperbolic Equation
AbstractIn this paper we consider a nonlinear nonlocal boundary value problem for one class of systems of hyperbolic equations with mixed...
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On a Boundary Value Problem for a Third-Order Equation of Parabolic-Hyperbolic Type with a Fractional Order Operator
AbstractIn the paper, we consider a boundary value problem for a third-order mixed differential equation of parabolic-hyperbolic type with a...
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On the Solvability of Initial and Boundary Value Problems for Abstract Functional-Differential Euler–Poisson–Darboux Equations
AbstractIn a Banach space, we consider the Cauchy problem and the Dirichlet and Neumann boundary value problems for a functional-differential...
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Boundary Value Problem with Parameter for Second-Order System of Hyperbolic Equations
AbstractThe paper devoted to the boundary value problem with parameter for second order system of hyperbolic equations. We study of a questions for...
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Analytical Solutions of Generalised Emden–Fowler Initial and Boundary Value Problems of Higher Order
In this paper, the analytical solutions of a class of generalised linear and nonlinear Emden–Fowler-type equations of higher order are presented...
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Analytical Solution of One Non-Local Problem for Hyperbolic Equation
AbstractIn this paper we consider small oscillations of the ideal gas near its equilibrium state inside an unbounded cylindrical tube. We investigate...
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THE BÄCKLUND TRANSFORMATION BETWEEN A COMMON SOLUTION OF BOTH LINEAR EQUATIONS IN THE LAX PAIR AND THE SOLUTION OF THE ASSOCIATED INITIAL-BOUNDARY VALUE PROBLEM FOR NONLINEAR EVOLUTION EQUATIONS ON THE HALF-LINE
We present a way to obtain a Bäcklund transformation (BT) from two linear equations on the half-line in the Lax pair. By the unique solvability of...
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Geometric Optics for Quasilinear Hyperbolic Boundary Value Problems
This paper presents the work in Kilque (2022) which investigate the existence of the leading profile of a WKB expansion for quasilinear initial...