Exponential Decay of Solutions for a Higher Order Wave Equation with Logarithmic Source Term

2018 ◽  
Author(s):  
Erhan Pişkin ◽  
Turgay Uysal ◽  
Shkelqim Hajrulla
Keyword(s):  
Wave Equation ◽  
Exponential Decay ◽  
Source Term ◽  
Higher Order ◽  
Decay Of Solutions

Exponential Decay of Global Solutions for some Quasilinear Higher-Order Wave Equation

2013 ◽  
Vol 336-338 ◽  
pp. 2233-2237
Author(s):  
Ren Bing Lin
Keyword(s):  
Wave Equation ◽  
Exponential Decay ◽  
Source Term ◽  
Global Solutions ◽  
Higher Order ◽  
Damping Term ◽  
Uniform Stabilization ◽  
Linear Damping

In this paper we prove the uniform stabilization of global solutions for some quasilinear higher-order wave equation with linear damping term and source term by applying a lemma due to V.Komornik.

scholarly journals Decay of solutions of the wave equation in expanding cosmological spacetimes

2019 ◽  
Vol 16 (01) ◽  
pp. 35-58
Author(s):  
João L. Costa ◽  
José Natário ◽  
Pedro F. C. Oliveira
Keyword(s):  
Wave Equation ◽  
Initial Data ◽  
Decay Rate ◽  
Time Derivative ◽  
Iteration Scheme ◽  
Higher Order ◽  
Accelerated Expansion ◽  
De Sitter ◽  
Decay Of Solutions ◽  
Partial Energy

We study the decay of solutions of the wave equation in some expanding cosmological spacetimes, namely flat Friedmann–Lemaître–Robertson–Walker (FLRW) models and the cosmological region of the Reissner–Nordström–de Sitter (RNdS) solution. By introducing a partial energy and using an iteration scheme, we find that, for initial data with finite higher order energies, the decay rate of the time derivative is faster than previously existing estimates. For models undergoing accelerated expansion, our decay rate appears to be (almost) sharp.

scholarly journals Exponential decay of solutions of a semilinear Lipschitz Perturbation of Kirchhoff-Carrier Wave Equation

1993 ◽  
Vol 15 (15) ◽  
pp. 17
Author(s):  
Eleni Bisognin
Keyword(s):  
Wave Equation ◽  
Mixed Problem ◽  
Exponential Decay ◽  
Lipschitz Function ◽  
Global Solutions ◽  
Work Study ◽  
Carrier Wave ◽  
Decay Of Solutions ◽  
Lipschitz Perturbation

In this work study the existence of global solutions and exponential decay of energy of the mixed problem for perturbed Kirchhoff-Carrier wave equationu" - M(a(u)) Δu + F(u) + γ u’ = fwhere F is a Lipschitz function.

scholarly journals Higher Order Wave Equation with Logarithmic Source Term

2017 ◽  
Author(s):  
Sh. Hajrulla ◽  
L. Bezati ◽  
F. Hoxha
Keyword(s):  
Wave Equation ◽  
Boundary Value Problem ◽  
Source Term ◽  
Boundary Value ◽  
Initial Boundary ◽  
Global Weak Solution ◽  
Initial Boundary Value Problem ◽  
Logarithmic Sobolev Inequality ◽  
Higher Order ◽  
Initial Boundary Value

In this paper we study the initial boundary value problem for logarithmic Higher Order Wave equation. Introducing the Logarithmic Sobolev inequality and using the combination of Galerkin method, we consider the theorem of existence of a global weak solution to problem for the initial boundary value problem of the logarithmic wave equation. By constructing an appropriate Lyapunov function, we obtain the decay estimates of energy for logarithmic Higher Order Wave equation. The proof of the main theorem is given.

Tensor mode perturbation of cosmology with higher order holonomy corrections

2016 ◽  
Vol 94 (9) ◽  
pp. 945-952
Author(s):  
Yu Li
Keyword(s):  
Wave Equation ◽  
Gravitational Wave ◽  
Quantum Cosmology ◽  
Source Term ◽  
Friedmann Equation ◽  
Mass Term ◽  
Higher Order ◽  
Quantum Corrections ◽  
Tensor Mode ◽  
Higher Order Corrections

In this paper, we discuss the tensor mode perturbation in the frame of loop quantum cosmology with higher order holonomy corrections. We get the dynamics of the background near the bounce and far from the bounce. Based on the solutions of the effective Friedmann equation, we deduce the effective gravitational wave equation and get the quantum corrections in both the mass term and source term. We solve the gravitational wave equation near the bounce and discuss the situation far from the bounce. We also find the new terms arose only when one considers the higher order corrections.

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