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On the Correctness of the Dirichlet Problem in a Characteristic Rectangle for Fourth Order Linear Hyperbolic Equations
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February 24, 2010
Abstract
It is proved that the Dirichlet problem is correct in the characteristic rectangle 𝐷𝑎𝑏 = [0, 𝑎] × [0, 𝑏] for the linear hyperbolic equation
with the summable in 𝐷𝑎𝑏 coefficients 𝑝0, 𝑝1, 𝑝2, 𝑝3 and 𝑞 if and only if the corresponding homogeneous problem has only the trivial solution. The effective and optimal in some sense restrictions on 𝑝0, 𝑝1, 𝑝2 and 𝑝3 guaranteeing the correctness of the Dirichlet problem are established.
Key words and phrases.: Fourth order linear hyperbolic equation; Dirichlet problem in the characteristic rectangle; correctness
Received: 1998-06-12
Published Online: 2010-02-24
Published in Print: 1999-October
© 1999 Plenum Publishing Corporation
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- Triple Positive Solutions for Multipoint Conjugate Boundary Value Problems
- A Problem with Nonlocal Boundary Conditions for a Quasilinear Parabolic Equation
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- Subsets of the Plane with Small Linear Sections and Invariant Extensions of the Two-Dimensional Lebesgue Measure
- On the Correctness of the Dirichlet Problem in a Characteristic Rectangle for Fourth Order Linear Hyperbolic Equations
- On Some Entire Modular Forms of an Integral Weight for the Congruence Subgroup Γ0(4𝑁)
- A Contact Problem of the Interaction of a Semi-Finite Inclusion with a Plate
Keywords for this article
Fourth order linear hyperbolic equation;
Dirichlet problem in the characteristic rectangle;
correctness
Articles in the same Issue
- Oscillation and Nonoscillation Criteria for a Second Order Linear Equation
- Triple Positive Solutions for Multipoint Conjugate Boundary Value Problems
- A Problem with Nonlocal Boundary Conditions for a Quasilinear Parabolic Equation
- On Bounded Solutions of Systems of Linear Functional Differential Equations
- Subsets of the Plane with Small Linear Sections and Invariant Extensions of the Two-Dimensional Lebesgue Measure
- On the Correctness of the Dirichlet Problem in a Characteristic Rectangle for Fourth Order Linear Hyperbolic Equations
- On Some Entire Modular Forms of an Integral Weight for the Congruence Subgroup Γ0(4𝑁)
- A Contact Problem of the Interaction of a Semi-Finite Inclusion with a Plate
