Exact solutions and branching of singularities for some hyperbolic equations in two variables

Richard Beals; Yakar Kannai

doi:10.1016/j.jde.2009.02.023

Exact solutions and branching of singularities for some hyperbolic equations in two variables

Richard Beals, Yakar Kannai

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Exact global propagators are constructed for the singular hyperbolic operators in two variables x^{2 k - 2} ∂_t² + λ (k - 1) x^{k - 2} ∂_t - ∂_x², λ a real parameter, and for the degenerate hyperbolic operators ∂_t² - t^{2 k - 2} ∂_x² - λ (k - 1) t^{k - 2} ∂_x. Qualitative phenomena such as uniqueness in the Cauchy problem and branching of singularities vary with λ, as shown earlier by Treves and by Taniguchi and Tozaki.

Original language	English
Pages (from-to)	3448-3470
Number of pages	23
Journal	Journal of Differential Equations
Volume	246
Issue number	9
DOIs	https://doi.org/10.1016/j.jde.2009.02.023
State	Published - 1 May 2009
Externally published	Yes

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abstract = "Exact global propagators are constructed for the singular hyperbolic operators in two variables x2 k - 2 ∂t2 + λ (k - 1) xk - 2 ∂t - ∂x2, λ a real parameter, and for the degenerate hyperbolic operators ∂t2 - t2 k - 2 ∂x2 - λ (k - 1) tk - 2 ∂x. Qualitative phenomena such as uniqueness in the Cauchy problem and branching of singularities vary with λ, as shown earlier by Treves and by Taniguchi and Tozaki.",

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AU - Kannai, Yakar

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AB - Exact global propagators are constructed for the singular hyperbolic operators in two variables x2 k - 2 ∂t2 + λ (k - 1) xk - 2 ∂t - ∂x2, λ a real parameter, and for the degenerate hyperbolic operators ∂t2 - t2 k - 2 ∂x2 - λ (k - 1) tk - 2 ∂x. Qualitative phenomena such as uniqueness in the Cauchy problem and branching of singularities vary with λ, as shown earlier by Treves and by Taniguchi and Tozaki.

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Exact solutions and branching of singularities for some hyperbolic equations in two variables

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