Nonlinear dissipative wave equations with space–time dependent potential

2011 ◽  
Vol 74 (12) ◽  
pp. 3945-3963 ◽  
Author(s):  
Maisa Khader
Keyword(s):  
Wave Equations ◽  
Space Time ◽  
Time Dependent ◽  
Dependent Potential

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 An exact solution of the Dirac equation for a time-dependent Hamiltonian in 1-1 dimension space-time

2010 ◽  
Vol 88 (2) ◽  
pp. 137-138 ◽  
Author(s):  
Dan Solomon
Keyword(s):  
Exact Solution ◽  
Dirac Equation ◽  
Space Time ◽  
Time Dependent ◽  
Dependent Potential ◽  
Dimension Space

We find an exact solution to the Dirac equation in 1–1 dimension space-time in the presence of a time-dependent potential that consists of a combination of electric, scalar, and pseudoscalar terms.

Decay of energy for wave equations with strong damping terms and space–time-dependent coefficients

2013 ◽  
Vol 93 (7) ◽  
pp. 1515-1532
Author(s):  
Andrew Carter ◽  
Terence Long ◽  
Davut Uǧurlu
Keyword(s):  
Wave Equations ◽  
Space Time ◽  
Time Dependent ◽  
Strong Damping
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