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The amount of non-uniqueness for factored equations with Euler-Poisson-Darboux factors (1997)

Goldstein, Jerome A. ; Lightbourne, James H. ; Sandefur, James T.

Chichester, West Sussex : Wiley-Blackwell

Mathematical Methods in the Applied Sciences 20 (1997), S. 1449-1457

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ISSN: 0170-4214

Keywords: Engineering ; Numerical Methods and Modeling

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Mathematics

Notes: Of concern are factored Euler-Poisson-Darboux equations of the type∏Nj=1(d2/dt2+(ρ/t)d/dt+Aj)u(t)=0,where, for example, Aj=-cjΔ, Δ being the Dirichlet Laplacian acting on L2(Ω), Ω⊂∝n, and 0〈c1〈…〈cN. More generally -Aj can be the square of the generator of a (C0) group on a Banach space. When the constant ρ is negative, the initial value problem for the factored EPD equation is ill-posed. Nevertheless, we determine how many initial conditions are necessary to guarantee uniqueness of a solution. This number jumps up as ρ crosses a negative integer from right to left. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Type of Medium: Electronic Resource

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