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On the Cauchy problem for the one-dimensional heat equation. (English) Zbl 0112.35201


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[1] H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, Oxford, at the Clarendon Press, 1947. · Zbl 0029.37801
[2] R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. · Zbl 0051.28802
[3] F. Ginsberg, On the Cauchy problem for the one-dimensional heat equation, Math. Comp. 17 (1963), 257 – 269. · Zbl 0112.35201
[4] J. Hadamard, Lectures on Cauchy’s Problem in Linear Partial Differential Equations, Dover Publications, N. Y., 1952. · Zbl 0049.34805
[5] E. Holmgren, “Sur l’extension de la methode d’integration de Riemann,” Ark. Mat. Fys., 1904.
[6] F. John, Comm. Pure Appl. Math., v. XIII, n. 4, November 1960.
[7] F. John, Numerical Solution of Problems which are not Well Posed in The Sense of Hadamard, NYU, (unpublished). · Zbl 0100.12701
[8] F. John, Partial Differential Equations–Lecture Notes, NYU 1952-53.
[9] L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa (3) 13 (1959), 115 – 162. · Zbl 0088.07601
[10] Carlo Pucci, On the improperly posed Cauchy problems for parabolic equations, Symposium on the numerical treatment of partial differential equations with real characteristics: Proceedings of the Rome Symposium (28-29-30 January 1959) organized by the Provisional International Computation Centre, Libreria Eredi Virgilio Veschi, Rome, 1959, pp. 140 – 144.
[11] James B. Scarborough, Numerical Mathematical Analysis, The Johns Hopkins Press, Baltimore, Md.; Oxford University Press, London, 1950. 2d ed. · Zbl 0040.21302
[12] J. Walsh, Interpolation and Approximation; AMS Colloquium Publications, American Mathematical Society, Rhode Island, 1956.
[13] E. Whittaker & J. Watson, Modern Analysis (Fourth Edition reprinted), Cambridge University Press, Cambridge, 1952.
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