a partial differential equation describing wave motion. It has the form ∇2φ = (1/c2) × (∂2φ/∂t2), where ∇2 is the Laplace operator, t the time, c the speed of propagation, and φ is a function characterizing the displacement of the wave
Examples of 'wave equation' in a sentence
wave equation
Also, we study the corresponding nonlinear wave equation.
S. S. Okoya 2000, 'On closed-form solutions of some nonlinear partial differential equations', International Journal of Mathematics and Mathematical Scienceshttp://dx.doi.org/10.1155/S0161171200001289. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
We consider the wave equation with a mild internal dissipation.
Mokhtar Kirane, Nasser-Eddine Tatar 1999, 'A memory type boundary stabilization of a mildly damped wave equation', Electronic Journal of Qualitative Theory of Differential Equationshttp://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=15. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
We study the first-order nonhomogenous wave equation.
Adem Kiliçman, Hassan Eltayeb 2007, 'A Note on Wave Equation and Convolutions', Differential Equations and Nonlinear Mechanicshttp://dx.doi.org/10.1155/2007/49251. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
This paper deals with a nonlinear viscoelastic wave equation with strong damping.
Xiaoming Peng, Xiaoxiao Zheng, Yadong Shang 2018, 'Lower bounds for the blow-up time to a nonlinear viscoelastic wave equation with strongdamping', AIMS Mathematicshttp://www.aimspress.com/article/10.3934/Math.2018.4.514/fulltext.html. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Two numerical algorithms are derived to compute the fractional diffusion-wave equation with a reaction term.
Hengfei Ding, Changpin Li 2013, 'Numerical Algorithms for the Fractional Diffusion-Wave Equation with Reaction Term',Abstract and Applied Analysishttp://dx.doi.org/10.1155/2013/493406. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
The sound propagation has to be described with a modified wave equation.
Mario WOLF, Elfgard KÜHNICKE 2015, 'Non-invasive and Locally Resolved Measurement of Sound Velocity by Ultrasound', Sensors & Transducershttp://www.sensorsportal.com/HTML/DIGEST/january_2015/Vol_184/P_2585.pdf. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Then, the differential equations decouple and sound propagation can be described bythe wave equation.
Bernd Baumann, Marcus Wolff, Bernd Kost, Hinrich Groninga 2007, 'Solving a coupled field problem by eigenmode expansion and finite element method',International Journal of Multiphysicshttp://journal.multiphysics.org/index.php/IJM/article/view/27. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Formulas for a particular solution of the inhomogeneous wave equation are derived.
Maciąg Artur 2005, 'Three-dimensional wave polynomials', Mathematical Problems in Engineeringhttp://www.hindawi.net/access/get.aspx?journal=mpe&volume=2005&pii=S1024123X05404044. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)