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Results tagged with hyperbolic-pde
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user 8799
Questions about partial differential equations of hyperbolic type. Often used in combination with the top-level tag ap.analysis-of-pdes.
16
votes
1
answer
761
views
The determinant as a differential operator
According to Gårding, the determinant is a hyperbolic polynomial over the space $\mathbf{Sym}_n$ of real symmetric $n\times n$ matrices. More precisely, it is hyperbolic in the direction of the identi …
- 52.3k
6
votes
1
answer
619
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A curious determinant of quadratic forms
In a work about the Wave Equation, I encountered the following symmetric matrix of size $1+n$, whose entries are quadratic forms. The arguments are a scalar $a$ and a vector $X\in k^n$.
$$S(a,X)=\beg …
- 52.3k
2
votes
0
answers
58
views
Convex solutions of linear hyperbolic PDEs in a planar domain
Consider a linear homogeneous 2nd-order PDE in a convex planar domain $\Omega$ :
$$a(x,y)\frac{\partial^2u}{\partial x^2}+2b(x,y)\frac{\partial^2u}{\partial x\partial y}+c(x,y)\frac{\partial^2u}{\part …
- 52.3k