scholarly journals Very weak solutions to hypoelliptic wave equations

2020 ◽  
Vol 268 (5) ◽  
pp. 2063-2088
Author(s):  
Michael Ruzhansky ◽  
Nurgissa Yessirkegenov
Keyword(s):  
Weak Solutions ◽  
Wave Equations ◽  
Very 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 Uniqueness of very weak solutions for a fractional filtration equation

2020 ◽  
Vol 365 ◽  
pp. 107041 ◽  
Author(s):  
Gabriele Grillo ◽  
Matteo Muratori ◽  
Fabio Punzo
Keyword(s):  
Weak Solutions ◽  
Very Weak Solutions ◽  
Filtration Equation

scholarly journals On very weak solutions to a class of double obstacle problems

2013 ◽  
Vol 402 (2) ◽  
pp. 702-709 ◽  
Author(s):  
Gejun Bao ◽  
Tingting Wang ◽  
Guanfeng Li
Keyword(s):  
Weak Solutions ◽  
Obstacle Problems ◽  
Very Weak Solutions

scholarly journals Very weak solutions of parabolic systems of p-Laplacian type

2002 ◽  
Vol 40 (1) ◽  
pp. 105-132 ◽  
Author(s):  
Juha Kinnunen ◽  
John L. Lewis
Keyword(s):  
Weak Solutions ◽  
Parabolic Systems ◽  
Very Weak Solutions
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