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Results tagged with hyperbolic-pde
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user 80602
Questions about partial differential equations of hyperbolic type. Often used in combination with the top-level tag ap.analysis-of-pdes.
3
votes
0
answers
124
views
Wave equation that becomes elliptic on a bounded domain (sign-changing coefficient)
I'm looking for results on this kind of problems:
$$ \partial_{tt}^2 u - \partial_x(a(x) \partial_x) = f,$$
$$u(t=0) = u_0, \quad \partial_t u(t=0) = u_1,$$
where $a$ changes sign: $a(x)= -c^2 < 0$ fo …
- 615
3
votes
1
answer
398
views
Does Huygens principle holds for heterogeneous media (variable coefficients)?
I'm having trouble to find references on that. Consider for instance a very simple model of a wave equation with variable coefficients:
$$\partial_{tt}^2 u(x,t) - \nabla \cdot( a(x) \nabla u(x,t)) = f …
- 615