The noncharacteristic Cauchy problem for parabolic equations in two space variables
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- by David Colton
- Proc. Amer. Math. Soc. 41 (1973), 551-556
- DOI: https://doi.org/10.1090/S0002-9939-1973-0324189-1
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Abstract:
An integral representation is obtained for the solution of the noncharacteristic Cauchy problem for second order parabolic equations in two space variables with entire, time independent coefficients. This is accomplished through the use of contour integration techniques and the calculus of residues in the space of several complex variables.References
- David Colton, Cauchy’s problem and the analytic continuation of solutions to elliptic equations, Symposium on Non-Well-Posed Problems and Logarithmic Convexity (Heriot-Watt Univ., Edinburgh, 1972) Lecture Notes in Math., Vol. 316, Springer, Berlin, 1973, pp. 55–66. MR 0399655
- C. Denson Hill, Parabolic equations in one space variable and the non-characteristic Cauchy problem, Comm. Pure Appl. Math. 20 (1967), 619–633. MR 214927, DOI 10.1002/cpa.3160200309
- C. Denson Hill, A method for the construction of reflection laws for a parabolic equation, Trans. Amer. Math. Soc. 133 (1968), 357–372. MR 235287, DOI 10.1090/S0002-9947-1968-0235287-8 L. Hörmander, Linear partial differential operators, Die Grundlehren der math. Wissenschaften, Band 116, Academic Press, New York; Springer-Verlag, Berlin, 1963. MR 28 #4221.
- Jan Persson, Linear Goursat problems for entire functions when the coefficients are variable, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 23 (1969), 87–98. MR 273174
Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 41 (1973), 551-556
- MSC: Primary 35C15; Secondary 35K10
- DOI: https://doi.org/10.1090/S0002-9939-1973-0324189-1
- MathSciNet review: 0324189