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.

**[1]**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) Springer, Berlin, 1973, pp. 55–66. Lecture Notes in Math., Vol. 316. MR**0399655****[2]**C. Denson Hill,*Parabolic equations in one space variable and the non-characteristic Cauchy problem*, Comm. Pure Appl. Math.**20**(1967), 619–633. MR**0214927****[3]**C. Denson Hill,*A method for the construction of reflection laws for a parabolic equation*, Trans. Amer. Math. Soc.**133**(1968), 357–372. MR**0235287**, 10.1090/S0002-9947-1968-0235287-8**[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]**Jan Persson,*Linear Goursat problems for entire functions when the coefficients are variable*, Ann. Scuola Norm. Sup. Pisa (3)**23**(1969), 87–98. MR**0273174**

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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