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On the parabolic equation \(sgn (x) | x | ^p u_y - u_{xx}=0\) and a related one. (English) Zbl 0274.35038

35K20 Initial-boundary value problems for second-order parabolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35A22 Transform methods (e.g., integral transforms) applied to PDEs
Full Text: DOI
[1] Baouendi, M. S.; Grisvard, P., Sur une equation d’evolution changeant de type, J. of Functional Analysis, 2, 352-369 (1968) · Zbl 0164.12701
[2] S. Bochner -K. Chandrasekharan,Fourier transforms, Annals of Mathematics Studies,19 (1949). · Zbl 0065.34101
[3] Erdélyi - Magnus - Oberhettinger - Tricomi,Tables of integral transforms, McGraw-Hill, 1954. · Zbl 0055.36401
[4] Fleming, W., A problem of random accelerations (1963), M.R.C. Rep.: U. S. Army Math. Center, Univ. of Wisconsin, M.R.C. Rep.
[5] M. Gévrey,Sur les équations aux dérivées partielles du type parabolique, chap. I, II, III, Journal de Mathématique (1913).
[6] M. Gévrey,Sur les équations aux dérivées partielles du type parabolique, chap. IV, V, Journal de Mathématique (1914), pp. 105-137. · JFM 45.0571.03
[7] Kohn, J. J.; Nirenberg, L., Degenerate elliptic-parabolic equations of second order, Comm. Pure and Appl. Math., 20, 797-872 (1967) · Zbl 0153.14503
[8] Lions, J. L.; Magenes, E., Problèmes aux limites non homogènes et applications (1968), Paris: Dunod, Paris · Zbl 0165.10801
[9] W. Magnus - F. Oberhettinger - R. P. Soni,Formulas and theorems for the special functions of mathematical physics, Springer, 1966. · Zbl 0143.08502
[10] D. S. Mitrinović,Analytic Inequalities, Springer, 1970. · Zbl 0199.38101
[11] Pagani, C. D., Su un problema di valori iniziali per una equazione parabolica singolare, Rend. Ist. Lombardo, 103, 618-653 (1969) · Zbl 0193.38901
[12] Pagani, C. D., Su alcune questioni connesse con l’equazione generalizzata di Fokker-Planck, Boll. U.M.I., 6, 961-986 (1970) · Zbl 0204.43201
[13] Pagani, C. D.; Talenti, G., On a forward-backward parabolic equation, Ann. Mat. Pura e Applicata, 90, 1-58 (1971) · Zbl 0238.35043
[14] E. Titchmarsh,Introduction to the theory of Fourier integrals, Oxford Univ. Press, 1948.
[15] G. N. Watson,Theory of Bessel Functions, Cambridge Univ. Press, 1958.
[16] A. H. Zemanian,Generalized integral transformations, Interscience Pub., 1968. · Zbl 0181.12701
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