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Spatial Problem of Darboux Type for One Model Equation of Third Order
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O. Jokhadze
Published/Copyright:
February 23, 2010
Abstract
For a hyperbolic type model equation of third order a Darboux type problem is investigated in a dihedral angle. It is shown that there exists a real number ρ0 such that for α > ρ0 the problem under consideration is uniquely solvable in the Frechet space. In the case where the coefficients are constants, Bochner's method is developed in multidimensional domains, and used to prove the uniquely solvability of the problem both in Frechet and in Banach spaces.
Key words and phrases.: Hyperbolic equation; Darboux type problem for the hyperbolic equation in the dihedral angle; characteristic plane; bicharacteristic line
Received: 1994-11-24
Published Online: 2010-02-23
Published in Print: 1996-December
© 1996 Plenum Publishing Corporation
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- On the Correctness of Nonlinear Boundary Value Problems for Systems of Generalized Ordinary Differential Equations
- Characterization of a Regular Family of Semimartingales by Line Integrals
- Non-Baire Unions in Category Bases
- Spatial Problem of Darboux Type for One Model Equation of Third Order
- On Continuous Extensions
- On Oscillation of Solutions of Second-Order Systems of Deviated Differential Equations
- Weighted LΦ Integral Inequalities for Maximal Operators
Articles in the same Issue
- On the Correctness of Nonlinear Boundary Value Problems for Systems of Generalized Ordinary Differential Equations
- Characterization of a Regular Family of Semimartingales by Line Integrals
- Non-Baire Unions in Category Bases
- Spatial Problem of Darboux Type for One Model Equation of Third Order
- On Continuous Extensions
- On Oscillation of Solutions of Second-Order Systems of Deviated Differential Equations
- Weighted LΦ Integral Inequalities for Maximal Operators
