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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
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.

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  • [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)
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Keywords: Integral representation, Cauchy problem, parabolic equation, characteristics, complex variables
Article copyright: © Copyright 1973 American Mathematical Society

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