In mathematics, a Petrovsky lacuna, named for the Russian mathematician I. G. Petrovsky, is a region where the

fundamental solution In mathematics, a fundamental solution for a linear partial differential operator is a formulation in the language of distribution theory of the older idea of a Green's function (although unlike Green's functions, fundamental solutions do not a ...

of a linear

hyperbolic partial differential equation In mathematics, a hyperbolic partial differential equation of order n is a partial differential equation (PDE) that, roughly speaking, has a well-posed initial value problem for the first n-1 derivatives. More precisely, the Cauchy problem can be ...

vanishes. They were studied by who found

topological In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...

conditions for their existence. Petrovsky's work was generalized and updated by .

References

*. *. *. *{{citation , last = Petrovsky , first = I.G. , author-link = Ivan Petrovsky , title = On the diffusion of waves and the lacunas for hyperbolic equations , year = 1945 , journal = Recueil Mathématique (Matematicheskii Sbornik) , volume=17 (59) , issue = 3 , pages=289–368 , url = http://mi.mathnet.ru/eng/msb/v59/i3/p289 , id = , mr = 16861 , zbl = 0061.21309. Hyperbolic partial differential equations Shock waves