# Questions tagged [hyperbolic-pde]

Questions about partial differential equations of hyperbolic type. Often used in combination with the top-level tag ap.analysis-of-pdes.

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### Does there exist an electromagnetic analogue of Einstein's field equations?

This will look like a physics question but it doesn't have anything to do with reality so its a vague math question if anything. I recently learned about gravitoelectromagnetism which describes an ...
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### The Cauchy problem in general relativity, hyperbolic PDEs, and Sobolev spaces on manifolds

(I apologize in advance if this question is ill-posed or not suitable for Math Overflow, I am not yet a research mathematician, just a student.) Let $(\Sigma,\bar{g})$ be an $n$-dimensional Riemannian ...
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### A PDE with boundary condition [closed]

I want to solve this PDE with boundary conditions $${u_{xy}} + y{u_y} = 0\,\,\,\,\,x > 0,y > 0\,,\,u\left( {x,0} \right) = {e^x},u\left( {0,y} \right) = \cos y$$ I did the following \begin{...
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### Nonlinear-PDE arising from flat conformal Chebyshev nets

Consider a flat, simply connected surface endowed with the Riemannian metric $g_0=e^{2\Omega(u,v)}\left(\mathbb{d}^2u +\mathbb{d}^2v \right)$, so that $\Omega(u,v)$ is an arbitrary harmonic function. ...
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### Scaling limit of transport equation with double-well potential

Let us consider the transport PDE $$u^\epsilon_t + u^\epsilon_x= -\frac{1}{\epsilon} W'(u^\epsilon)$$ where $W$ is a double-well potential -- for example, $W(x)=\frac{1}{4}(x^2-1)^2$ so that the PDE ...
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