A semilinear wave equation with space-time dependent coefficients and a memory boundarylike antiperiodic condition: Regularity and stability

2010 ◽  
Vol 51 (10) ◽  
pp. 103504 ◽  
Author(s):  
Út V. Lê
Keyword(s):  
Wave Equation ◽  
Space Time ◽  
Time Dependent ◽  
Semilinear Wave Equation

scholarly journals A minimization approach to the wave equation on time-dependent domains

2020 ◽  
Vol 13 (4) ◽  
pp. 425-436 ◽  
Author(s):  
Gianni Dal Maso ◽  
Lucia De Luca
Keyword(s):  
Wave Equation ◽  
Weak Solutions ◽  
Space Time ◽  
Time Dependent ◽  
Existence Of Weak Solutions ◽  
Homogeneous Wave ◽  
Minimization Approach ◽  
Homogeneous Wave Equation

AbstractWe prove the existence of weak solutions to the homogeneous wave equation on a suitable class of time-dependent domains. Using the approach suggested by De Giorgi and developed by Serra and Tilli, such solutions are approximated by minimizers of suitable functionals in space-time.

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 $t\to \infty$ .

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