scholarly journals The Influence of Oscillations on Energy Estimates for Damped Wave Models with Time-dependent Propagation Speed and Dissipation

2019 ◽  
pp. 275-316 ◽  
Author(s):  
Halit Sevki Aslan ◽  
Michael Reissig
Keyword(s):  
Propagation Speed ◽  
Time Dependent ◽  
Energy Estimates ◽  
Wave Models

Theory of damped wave models with integrable and decaying in time speed of propagation

2016 ◽  
Vol 13 (02) ◽  
pp. 417-439 ◽  
Author(s):  
Marcelo Rempel Ebert ◽  
Michael Reissig
Keyword(s):  
Cauchy Problem ◽  
Wave Equations ◽  
Propagation Speed ◽  
Time Dependent ◽  
Scale Invariant ◽  
The Cauchy Problem ◽  
Wave Models ◽  
Speed Of Propagation ◽  
Loss Of Regularity

We study the Cauchy problem for damped wave equations with a time-dependent propagation speed and dissipation. The model of interest is [Formula: see text] We assume [Formula: see text]. Then we propose a classification of dissipation terms in non-effective and effective. In each case we derive estimates for kinetic and elastic type energies by developing a suitable WKB analysis. Moreover, we show optimality of results by the aid of scale-invariant models. Finally, we explain by an example that in some estimates a loss of regularity appears.

scholarly journals Global existence and decay estimates for nonlinear wave equations with space-time dependent dissipative term

2015 ◽  
Vol 12 (02) ◽  
pp. 249-276
Author(s):  
Tomonari Watanabe
Keyword(s):  
Global Existence ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Space Time ◽  
Time Dependent ◽  
Nonlinear Wave Equations ◽  
Energy Estimates ◽  
Space Region ◽  
Decay Estimates ◽  
Dissipative Term

We study the global existence and the derivation of decay estimates for nonlinear wave equations with a space-time dependent dissipative term posed in an exterior domain. The linear dissipative effect may vanish in a compact space region and, moreover, the nonlinear terms need not be in a divergence form. In order to establish higher-order energy estimates, we introduce an argument based on a suitable rescaling. The proposed method is useful to control certain derivatives of the dissipation coefficient.

scholarly journals Time-variability of the Crab Nebula wisps

2000 ◽  
Vol 177 ◽  
pp. 507-508 ◽  
Author(s):  
Anatoly Spitkovsky ◽  
Jonathan Arons
Keyword(s):  
Magnetic Field ◽  
Crab Nebula ◽  
Propagation Speed ◽  
Time Dependent ◽  
Time Variability ◽  
Electron Positron ◽  
Pair Density ◽  
Pulsar Wind ◽  
The Crab Nebula ◽  
The Waves

AbstractWe present results of time-dependent numerical modeling of the internal structure of the collisionless shock terminating the pulsar wind in Crab Nebula. We treat the equatorial relativistic wind as composed of ions and electron-positron plasma with an embedded toroidal magnetic field. Relativistic cyclotron instability of the ion ring downstream from the shock is found to launch outward propagating magnetosonic waves. Due to the fresh supply of ions crossing the shock, the time-dependent process achieves a limit-cycle pattern, in which the waves are launched with periodicity on the order of the ion Larmor time. Compressions in magnetic field and pair density associated with these waves as well as their propagation speed qualitatively reproduce the features observed in the wisps.

Global existence of small data solutions for wave models with sub-exponential propagation speed

2015 ◽  
Vol 129 ◽  
pp. 173-188 ◽  
Author(s):  
Tang Bao Ngoc Bui ◽  
Michael Reissig
Keyword(s):  
Global Existence ◽  
Propagation Speed ◽  
Small Data ◽  
Wave Models
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