$L^p$ estimates for the linear wave equation and global existence for semilinear wave equations in exterior domains

2001 ◽  
Vol 320 (1) ◽  
pp. 11-31 ◽  
Author(s):  
Mitsuhiro Nakao
Keyword(s):  
Wave Equation ◽  
Global Existence ◽  
Wave Equations ◽  
Linear Wave ◽  
Exterior Domains ◽  
Linear Wave Equation ◽  
Semilinear Wave Equations

scholarly journals Scattering for critical wave equations with variable coefficients

2021 ◽  
pp. 1-19
Author(s):  
Shi-Zhuo Looi ◽  
Mihai Tohaneanu
Keyword(s):  
Wave Equation ◽  
Wave Equations ◽  
Variable Coefficients ◽  
Energy Decay ◽  
Time Dependent ◽  
Linear Wave ◽  
Decay Estimates ◽  
Local Energy ◽  
Linear Wave Equation ◽  
Semilinear Wave Equation

Abstract We prove that solutions to the quintic semilinear wave equation with variable coefficients in ${{\mathbb {R}}}^{1+3}$ scatter to a solution to the corresponding linear wave equation. The coefficients are small and decay as $|x|\to \infty$ , but are allowed to be time dependent. The proof uses local energy decay estimates to establish the decay of the $L^{6}$ norm of the solution as $t\to \infty$ .

scholarly journals ON THE NONRELATIVISTIC LIMIT OF LINEAR WAVE EQUATIONS FOR ZERO AND UNITY SPIN PARTICLES

2008 ◽  
Vol 23 (02) ◽  
pp. 129-137 ◽  
Author(s):  
P. YU. MOSHIN ◽  
J. L. TOMAZELLI
Keyword(s):  
Wave Equation ◽  
Power Series ◽  
Unitary Transformation ◽  
Wave Equations ◽  
Power Series Expansion ◽  
Particle Dynamics ◽  
Nonrelativistic Limit ◽  
Linear Wave ◽  
Linear Wave Equation ◽  
Linear Wave Equations

The nonrelativistic limit of the linear wave equation for zero and unity spin bosons of mass m in the Duffin–Kemmer–Petiau representation is investigated by means of a unitary transformation, analogous to the Foldy–Wouthuysen canonical transformation for a relativistic electron. The interacting case is also analyzed, by considering a power series expansion of the transformed Hamiltonian, thus demonstrating that all features of particle dynamics can be recovered if corrections of order 1/m2 are taken into account through a recursive iteration procedure.

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