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The noncharacteristic Cauchy problem for parabolic equations in two space variables


Author: David Colton
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
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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 [Enhancements On Off] (What's this?)

  • [1] D. Colton, Cauchy's problem and the analytic continuation of solutions to elliptic equations, Proc. Sympos. Non-Well Posed Problems and Logarithmic Convexity, Springer-Verlag Lecture Note Series, vol. 316, 1973, pp. 55-66. MR 0399655 (53:3498)
  • [2] C. D. Hill, Parabolic equations in one space variable and the non-characteristic Cauchy problem, Comm. Pure Appl. Math. 20 (1967), 619-633. MR 35 #5774. MR 0214927 (35:5774)
  • [3] -, A method for the construction of reflection laws for a parabolic equation, Trans. Amer. Math. Soc. 133 (1968), 357-372. MR 38 #3597. MR 0235287 (38:3597)
  • [4] L. Hörmander, Linear partial differential operators, Die Grundlehren der math. Wissenschaften, Band 116, Academic Press, New York; Springer-Verlag, Berlin, 1963. MR 28 #4221.
  • [5] J. Persson, Linear Goursat problems for entire functions when the coefficients are variable, Ann. Scuola Norm. Sup. Pisa (3) 23 (1969), 87-98. MR 42 #8055. MR 0273174 (42:8055)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0324189-1
Keywords: Integral representation, Cauchy problem, parabolic equation, characteristics, complex variables
Article copyright: © Copyright 1973 American Mathematical Society

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