State of the Art of Low‐Frequency Acoustic Modulation: Intensity Enhancement and Directional Control
Advanced Science, EarlyView.High intensity low‐frequency sound sources hold significant value in many fields. However, their long wavelength, strong penetrability, and tendency to diffract make direction control and intensity enhancement challenging. Acoustic generators and metamaterial‐based acoustic devices still face issues such as low energy efficiency, poor directional ...
Jingsong Xu +13 more
wiley +1 more source
On equivalence of entropy and viscosity solutions to degenerate parabolic equations and applications [PDF]
arXivHere, we consider anisotropic degenerate parabolic-hyperbolic equations and degenerate quasilinear Hamilton-Jacobi equations. We prove the equivalence of two notions of entropy and viscosity solutions of two equations, and apply it to obtain a large-time behavior of viscosity solutions to quasilinear Hamilton-Jacobi equations, and entropy solutions to ...
arxiv
Weak Solution of a Doubly Degenerate Parabolic Equation [PDF]
arXiv, 2016 This paper studies a fourth-order, nonlinear, doubly-degenerate parabolic equation derived from the thin film equation in spherical geometry. A regularization method is used to study the equation and several useful estimates are obtained. The main result of this paper is to prove the existence of a weak solution of the equation in a weighted Sobolev ...
arxiv
On the Cauchy problem and initial traces for a degenerate parabolic equation
, 1989 The authors study the Cauchy problem for the degenerate parabolic equation ut = div(|Du| p−2 Du ...
E. Benedetto, M. A. Herrero
semanticscholar +1 more source
Electrostatically Reinforced Double Network Granular Hydrogels
Advanced Science, EarlyView.Electrostatically reinforced double network granular hydrogels (DNGHs) with cartilage‐like fracture energy are introduced. An empirical model predicts the composition‐dependent fracture energy based on dissipation zone size, contact area, and inter‐particle adhesion energy. Thanks to their granular structure and the inter‐particle attraction, the DNGHs
Tianyu Yuan +3 more
wiley +1 more source
Homogenization of a nonlinear degenerate parabolic differential equation
Electronic Journal of Differential Equations, 2001 In this article, we study the homogenization of the nonlinear degenerate parabolic equation $$ partial_t b({x /varepsilon},u_varepsilon) - mathop{ m div} a({x /varepsilon},{t /varepsilon}, u_varepsilon,abla u_varepsilon)=f(x,t), $$ with mixed boundary ...
A. K. Nandakumaran, M. Rajesh
doaj
Abstract elliptic and parabolic equatıons in Morrey spaces and applications [PDF]
arXiv, 2019 We presents the study the separability properties for differential-operator equations in Morrey spaces. We prove that the corresponding differential operator is a generator of analytic semigroup in vector-valued Morrey spaces. Moreover, maximal regularity properties of corresponding parabolic equation {\i}s obtained.
arxiv
Folding of set-theoretical solutions of the Yang-Baxter equation
, 2010 We establish a correspondence between the invariant subsets of a non-degenerate symmetric set-theoretical solution of the quantum Yang-Baxter equation and the parabolic subgroups of its structure group, equipped with its canonical Garside structure ...
Chouraqui, Fabienne, Godelle, Eddy
core +1 more source
The asymptotic behavior of the solutions of degenerate parabolic equations [PDF]
, 1987 Catherine Bandle +2 more
openalex +1 more source
Parametrix for a degenerate parabolic equation [PDF]
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1979 Iwasaki, Chisato, Iwasaki, Nobuhisa
openaire +2 more sources