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, 2021 In this chapter, partial differential equations that govern many featured wave propagation phenomena are discussed. We start with modelling the process of string vibration through a partial differential equation, known as the wave equation, or the equation for string vibration. Then the concepts of initial and boundary conditions are introduced.
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On the local fractional wave equation in fractal strings
Mathematical methods in the applied sciences, 2019The key aim of the present study is to attain nondifferentiable solutions of extended wave equation by making use of a local fractional derivative describing fractal strings by applying local fractional homotopy perturbation Laplace transform scheme. The
Jagdev Singh +3 more
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Vibration Acoustics Applied to VVER-1200 Reactor Plant, 2017
One dimensional second-order hyperbolic wave equation(Classical wave equation) u c u tt xx = 2 One dimensional first-order hyperbolic linear convection equation u cu t x + = 0 it describes a wave propagating in x direction with velocity C.
Romain Boman
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One dimensional second-order hyperbolic wave equation(Classical wave equation) u c u tt xx = 2 One dimensional first-order hyperbolic linear convection equation u cu t x + = 0 it describes a wave propagating in x direction with velocity C.
Romain Boman
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Trefftz discontinuous Galerkin methods on unstructured meshes for the wave equation
, 2015We describe and analyse a space-time Trefftz discontinuous Galerkin method for the wave equation. The method is defined for unstructured meshes whose internal faces need not be aligned to the space-time axes.
A. Moiola
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On the wave equation with a potential
Communications in Partial Differential Equations, 1999We prove Strichartz estimates for wave equations with a ...
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Variations on the wave equation [PDF]
Mathematical Methods in the Applied Sciences, 2001 AbstractA lot of vibration processes in mathematical physics are described by the wave equation or by related equations and systems, and plenty of research has been done on this subject. The results and methods obtained thereby have been very important in other fields of application, and they still are. They also had and still have an immense influence
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2001
In this chapter we study the wave equation $$u_{tt} = \Delta u$$ on an open subset \(\Omega\) of \(\mathbb{R}^n.\)
Frank Neubrander +3 more
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In this chapter we study the wave equation $$u_{tt} = \Delta u$$ on an open subset \(\Omega\) of \(\mathbb{R}^n.\)
Frank Neubrander +3 more
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, 2014
This paper concludes the series begun in [M. Dafermos and I. Rodnianski, Decay for solutions of the wave equation on Kerr exterior spacetimes I-II: the cases |a|
Mihalis Dafermos +2 more
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This paper concludes the series begun in [M. Dafermos and I. Rodnianski, Decay for solutions of the wave equation on Kerr exterior spacetimes I-II: the cases |a|
Mihalis Dafermos +2 more
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Stable numerical coupling of exterior and interior problems for the wave equation
Numerische Mathematik, 2013The acoustic wave equation on the whole three-dimensional space is considered with initial data and inhomogeneity having support in a bounded domain, which need not be convex.
L. Banjai, C. Lubich, F. Sayas
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2014
Waves occur in various forms such as longitudinal acoustic waves in a medium such as air, transverse waves in a string, waves in a membrane and as electromagnetic radiation. All these are governed by the wave equation with the dependent variable being pressure or displacement or electric field etc.
S.P. Venkateshan, Prasanna Swaminathan
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Waves occur in various forms such as longitudinal acoustic waves in a medium such as air, transverse waves in a string, waves in a membrane and as electromagnetic radiation. All these are governed by the wave equation with the dependent variable being pressure or displacement or electric field etc.
S.P. Venkateshan, Prasanna Swaminathan
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