Forced oscillations for the solutions of a nonlinear hyperbolic equation

1982 ◽  
Vol 6 (3) ◽  
pp. 209-216 ◽  
Author(s):  
M.A. Prestel
Keyword(s):  
Hyperbolic Equation ◽  
Forced Oscillations ◽  
Nonlinear Hyperbolic Equation

On Solvability and Well-Posedness of Boundary Value Problems for Nonlinear Hyperbolic Equations of the Fourth Order

2008 ◽  
Vol 15 (3) ◽  
pp. 555-569
Author(s):  
Tariel Kiguradze
Keyword(s):  
Hyperbolic Equation ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Hyperbolic Equations ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Nonlinear Hyperbolic Equation ◽  
Well Posedness ◽  
Nonlinear Hyperbolic Equations ◽  
Right Hand

Abstract In the rectangle Ω = [0, a] × [0, b] the nonlinear hyperbolic equation 𝑢(2,2) = 𝑓(𝑥, 𝑦, 𝑢) with the continuous right-hand side 𝑓 : Ω × ℝ → ℝ is considered. Unimprovable in a sense sufficient conditions of solvability of Dirichlet, Dirichlet–Nicoletti and Nicoletti boundary value problems are established.

scholarly journals Asymptotic Behavior of Solutions to the Damped Nonlinear Hyperbolic Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Yu-Zhu Wang
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Hyperbolic Equation ◽  
Contraction Mapping ◽  
Dimensional Space ◽  
Contraction Mapping Principle ◽  
Nonlinear Hyperbolic Equation ◽  
Asymptotic Behavior Of Solutions ◽  
Initial Value ◽  
The Cauchy Problem

We consider the Cauchy problem for the damped nonlinear hyperbolic equation inn-dimensional space. Under small condition on the initial value, the global existence and asymptotic behavior of the solution in the corresponding Sobolev spaces are obtained by the contraction mapping principle.

scholarly journals On the flow of polythermal glaciers. II. Surface wave analysis

1980 ◽  
Vol 370 (1741) ◽  
pp. 155-171 ◽  
Keyword(s):  
Surface Wave ◽  
Hyperbolic Equation ◽  
Large Scale ◽  
Reduced Model ◽  
Nonlinear Hyperbolic Equation ◽  
Wave Analysis ◽  
Valley Glacier ◽  
Kinematic Waves ◽  
Surface Disturbance ◽  
Formation And Evolution

We show how the ‘reduced’ model developed in part I of this paper may be used to derive a nonlinear hyperbolic equation which describes the passage of kinematic waves along the surface of a valley glacier. Qualitative descriptions of large-scale snout movements and the formation and evolution of surface shocks are found from this approach, and earlier results of Nye (1960) are reproduced in the limit where surface disturbance amplitudes are ‘small’.

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