# Questions tagged [wave-equation]

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### EM-wave equation in matter from Lagrangian

Note I am not sure if this post is of relevance for this platform, but I already asked the question in Physics Stack Exchange and in Mathematics Stack Exchange without success. Setup Let's suppose a ...
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### Does the self inductance and velocity factor of the elements of a dipole antenna change its resonant frequency?

I've asked this question on Ham Stack Exchange but no one knows the answer so i thought would try posting on this site. Below are well known equations from Wikipedia for the resistance and reactance ...
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### Fractional derivative notation in wave turbulence

This is my first question in MathOverflow and I will do my best to format it correctly and make it clear. I am reading a paper on dispersive wave turbulence which introduces the following family of ...
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### Classification of homogeneous distributions

On page 92 of these notes, there is a discussion on how to find the fundamental solution to the D'Alembertian operator. It is firstly proposed that $c_n(t^2 - |x|^2 )^{-(n-1)/2}$ may be a good ...
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### A question for regularity of solutions to wave equation

let $T>0$ and suppose $\Omega$ is a bounded domain with smooth boundary. Let $g \in L^\infty(0,T;H^1(\partial \Omega))$ and consider the wave equation \label{pf0} \begin{aligned} \...
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### wave equation with L^2 boundary data via spectral decomposition

It is classical that if $\Omega \subset \mathbb R^n$ is a bounded domain with smooth boundary, then the equation \label{pf2} \begin{aligned} \begin{cases} \partial^2_{t}u- \Delta u=0\,\...
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### Wellposedness of semilinear wave equation with discontinuous source

Where can I find existence and uniqueness results for semilinear wave equations with discontinuous, i.e. $$\partial^2_{tt} u - \Delta u = f(u), \quad t >0, \ x \in \Omega$$ where $f$ is ...
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### Initial-boundary value problem for the damped wave equation with nonlinear source (in bounded domains)

It is well known that the initial-value problem for the wave equation on $\mathbb R^N$ can be studied by means of Fourier transform. What reference presents well-posedness results and qualitative ...
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### Wave equation with porous medium term

The classical porous media equation is $$u_t + \Delta(u^m) = 0 \quad m>1.$$ Has the (degenerate) wave equation $$u_{tt} + \Delta(u^m) = 0$$ been subject of studies? What would the physical ...
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### Is the exact solution of the wave equation for the scattering of waves by a disk/cylinder an open problem?

The solution exact solution of the Helmholtz equation for the scattering of waves by a sphere is relatively straightforward and has been known since the time of Lord Rayleigh. The exact solution of ...
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### Well-posedness of wave equations with time-dependent coefficient

Let us consider the following wave equation \begin{array}{rrr} y_{tt}=y_{xx}+a(t,x)y_{t} & \text{in} & (0,T)\times (0,1), \\ y(0,t)=0\text{ , }y(t,1)=0 & \text{in} & (0,T), \\ y(0,x)...
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### Wave equation with 'spring' integral boundary condition

I am really stuck with this small toy problem. I am trying to solve a wave equation on unit interval $x \in [0,1]$ with a specific boundary condition which I can't see how to tackle. The problem is: ...