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A Uniqueness Theorem on the Degenerate Cauchy Problem(1)

Published online by Cambridge University Press:  20 November 2018

Chung-Lie Wang
Chung-Lie Wang*
Affiliation:
University of Regina, Regina, Saskatchewan
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In [4] Carroll and the author have treated the following problem

(1)

where Λ is a closed densely defined self-adjoint operator in a separable Hilbert space H with (Λu, u) ≥ c ‖u‖2, c > 0, Λ-1 ∊ L(H) (L(E, F) is the space of continuous linear maps from E to F; in particular, L(H) = L(H, H)), a(t) > 0 for t > 0 a(0) = 0 and S(t), R(t), B(t) ∈ L(H).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 3 , August 1975 , pp. 417 - 421
Copyright
Copyright © Canadian Mathematical Society 1975

Footnotes

(1)

Supported (in part) by a National Research Council of Canada Grant A3116.

References

1. Carroll, R., Some degenerate Cauchy Problems with operator coefficients, Pacific J. Math., 13 (1963), 471-485.Google Scholar
2. Carroll, R. On the singular Cauchy Problem, J. Math, and Mech., 12 (1963), 69-102.Google Scholar
3. Carroll, R. on the spectral determination of the Green's operator, J. Math, and Mech., 15 (1966), 1003-1018.Google Scholar
4. Carroll, R. and Wang, C. L., On the degenerate Cauchy Problem, Can. J. Math., 17 (1965), 245-256.Google Scholar
5. Coddington, E. and Levinson, N., Theory of ordinary differential equations, McGraw-Hill, New York, 1955.Google Scholar
6. Dieudonne, J., Foundations of modern analysis, Academic Press, New York, 1960.Google Scholar
7. Krasnov, M., Mixed boundary value problem for degenerate linear hyperbolic differential equations of the second order, Mat. Sbornik, 49 (81) (1959), 29-84.Google Scholar
8. Protter, M., The Cauchy Problem for a hyperbolic second order equation with data on the parabolic line, Can. J. Math., 6 (1954), 542-553.Google Scholar
9. Rickart, C., General Theory of Banach algebras, Van Nostrand, Princeton, 1960.Google Scholar
10. Wang, C. L., On the degenerate Cauchy Problem for linear hyperbolic equations of the second order, Rutgers, The State University, Ph.D. Thesis (1964).Google Scholar