Convergence of bounded weak solutions of the wave equation with dissipation and analytic nonlinearity

1999 ◽  
Vol 9 (2) ◽  
pp. 95-124 ◽  
Author(s):  
Alain Haraux ◽  
Mohamed Ali Jendoubi
Keyword(s):  
Wave Equation ◽  
Weak Solutions ◽  
Analytic Nonlinearity ◽  
Bounded Weak Solutions

scholarly journals Fractional wave equations with attenuation

2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Peter Straka ◽  
Mark Meerschaert ◽  
Robert McGough ◽  
Yuzhen Zhou
Keyword(s):  
Wave Equation ◽  
Power Law ◽  
Weak Solutions ◽  
Wave Equations ◽  
Inhomogeneous Media ◽  
Medical Ultrasound ◽  
Sound Waves ◽  
Fractional Wave Equations

AbstractFractional wave equations with attenuation have been proposed by Caputo [5], Szabo [28], Chen and Holm [7], and Kelly et al. [11]. These equations capture the power-law attenuation with frequency observed in many experimental settings when sound waves travel through inhomogeneous media. In particular, these models are useful for medical ultrasound. This paper develops stochastic solutions and weak solutions to the power law wave equation of Kelly et al. [11].

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 Real-valued, time-periodic localized weak solutions for a semilinear wave equation with periodic potentials

Nonlinearity ◽  
2019 ◽  
Vol 32 (4) ◽  
pp. 1408-1439 ◽  
Author(s):  
Andreas Hirsch ◽  
Wolfgang Reichel
Keyword(s):  
Wave Equation ◽  
Weak Solutions ◽  
Semilinear Wave Equation ◽  
Periodic Potentials ◽  
Time Periodic

Weak Solutions to a Nonlinear Variational Wave Equation

2003 ◽  
Vol 166 (4) ◽  
pp. 303-319 ◽  
Author(s):  
Ping Zhang ◽  
Yuxi Zheng
Keyword(s):  
Wave Equation ◽  
Weak Solutions ◽  
Variational Wave

Local Hölder regularity for a doubly singular PDE

2018 ◽  
Vol 22 (03) ◽  
pp. 1850054
Author(s):  
Eurica Henriques
Keyword(s):  
Parabolic Equation ◽  
Weak Solutions ◽  
Iteration Method ◽  
Hölder Continuity ◽  
Hölder Regularity ◽  
Holder Continuity ◽  
Singular Parabolic Equation ◽  
Local Hölder Continuity ◽  
Singular Pde ◽  
Bounded Weak Solutions

We establish the local Hölder continuity for the nonnegative bounded weak solutions of a certain doubly singular parabolic equation. The proof involves the method of intrinsic scaling and the parabolic version of De Giorgi’s iteration method.

Global-in-time bounded weak solutions to a degenerate quasilinear Keller–Segel system with rotation

Nonlinearity ◽  
2014 ◽  
Vol 27 (8) ◽  
pp. 1899-1913 ◽  
Author(s):  
Xinru Cao ◽  
Sachiko Ishida
Keyword(s):  
Weak Solutions ◽  
Bounded Weak Solutions
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