×

Hyperbolic potential theory. (English) Zbl 0263.35055


MSC:

35L05 Wave equation
35L20 Initial-boundary value problems for second-order hyperbolic equations
35C15 Integral representations of solutions to PDEs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Carroll, R., Abstract Methods in Partial Differential Equations, New York: Harper & Row 1969. · Zbl 0193.06501
[2] Courant, R., & D. Hilbert, Methods of Mathematical Physics, vol. II, New York: John Wiley & Sons (Interscience) 1962. · Zbl 0099.29504
[3] Friedman, A., Partial Differential Equations of Parabolic Type. Englewood-Cliffs, New Jersey: Prentice-Hall 1964. · Zbl 0144.34903
[4] Günter, N., Potentialtheorie, Leipzig: B. G. Teubner 1957.
[5] Hadamard, J., Lectures on Cauchy’s Problem in Linear Partial Differential Equation, New York: Dover Publications 1952. · Zbl 0049.34805
[6] Hörmander, L., Linear Partial Differential Operators, Berlin-Göttingen-Heidelberg: Springer 1963. · Zbl 0108.09301
[7] Il’in, V. A., On the solvability of mixed problems for hyperbolic and parabolic equations, translated from Uspehi Mat. Nauk 15 (2), 97-154 (1960) as Russian Math. Surveys 15 (2), 85-142 (1960).
[8] John, F., Solutions of second order hyperbolic differential equations with constant coefficients in a domain with a plane boundary, Comm. Pure and Appl. Math. 7, 245-269 (1954). · Zbl 0057.32601 · doi:10.1002/cpa.3160070202
[9] John, F., Differential equations with approximate and improper data, N.Y.U. lecture notes, 1954-1955, no. 44.
[10] Kellogg, O. D., Foundations of Potential Theory, New York: Dover Publications 1953. · Zbl 0053.07301
[11] Kreiss, H. O., Initial boundary value problems for hyperbolic systems, Comm. Pure Appl. Math. 23, 277-298 (1970). · Zbl 0193.06902 · doi:10.1002/cpa.3160230304
[12] Ladyzhenskaya, O. A., The mixed problem for hyperbolic equations, Gostekhizdat. Moscow 1953 (in Russian). · Zbl 0052.32501
[13] Müntz, Ch. H., Zum dynamischen Wärmeleitungsproblem, Math. Z. 38, 323-337 (1933). · JFM 60.1139.07 · doi:10.1007/BF01170641
[14] Ralston, J. V., Note on a paper of Kreiss, Comm. Pure Appl. Math. 24 (6), 759-762 (1971). · Zbl 0215.16802 · doi:10.1002/cpa.3160240603
[15] Rosenbloom, P. C., The linearized theory of supersonic flow about a thin airfoil. Proc. Third Midwestern Conference on Fluid Mechanics, University of Minnesota, 1953. · Zbl 0052.08403
[16] Slobodetski, L. N., The theory of potentials for parabolic equations, Doklady Akad. Nauk SSSR 103, 19-22 (1955) (in Russian).
[17] Tychonoff, A., Sur l’équation de la chaleur à plusieurs variables, Vull, Univ. Etat. Moscow, Ser. Int., Sect. A. Math. Mécan. No. 1, 1-44 (1938). · Zbl 0024.11201
[18] Wendland, W., Die Behandlung von Randwertaufgaben im R3 mit Hilfe von Einfach- und Doppelschichtpotentialen, Numerische Mathematik 11, 380-404 (1968). · Zbl 0165.18401 · doi:10.1007/BF02161886
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.