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References
S. Bergman, Integral Operators in the Theory of Linear Partial Differential Equations, Springer-Verlag, Berlin, 1961.
S. Bergman, Operator methods in the theory of compressible fluids, Proceedings of Symposia in Applied Mathematics, American Mathematical Society, Providence, Rhode Island, Vol. 1, 1949, 19–40.
S. Bergman, On singularities of solutions of certain differential equations in three variables, Trans. Amer. Math. Soc. 85 (1957), 462–488.
S. Bergman and M. Schiffer, Kernel Functions and Differential Equations in Mathematical Physics, Academic Press, New York, 1953.
D. Colton, Integral Operators and reflection principles for parabolic equations in one space variable, J. Diff. Eqns., to appear.
D. Colton, Generalized reflection principles for parabolic equations in one space variable, Duke Math. J., to appear.
D. Colton, The non-characteristic Cauchy problem for parabolic equations in one space variable, SIAM J. Math. Anal., to appear.
D. Colton, The approximation of solutions to initial-boundary value problems for parabolic equations in one space variable, submitted for publication.
A. Friedman, Partial Differential Equations of Parabolic Type, Prentice Hall, Englewood Cliffs, New Jersey, 1964.
P. R. Garabedian, An example of axially symmetric flow with a free surface, Studies in Mathematics and Mechanics Presented to Richard von Mises, Academic Press, New York, 1954, 149–159.
R. P. Gilbert, Function Theoretic Methods in Partial Differential Equations, Academic Press, New York, 1969.
R. P. Gilbert, Constructive Methods for Elliptic Partial Differential Equations, Springer-Verlag Lecture Note Series, Berlin, to appear.
C. D. Hill, A method for the construction of reflection laws for a parabolic equation, Trans. Amer. Math. Soc. 20 (1967), 357–372.
C. D. Hill, Parabolic equations in one space variable and the non-characteristic Cauchy problem, Comm. Pure. Appl. Math. 20 (1967), 619–633.
H. Lewy, On the reflection laws of second order differential equations in two independent variables, Bull. Amer. Math. Soc. 65 (1959), 37–58.
A. V. Luikov, Analytical Heat Diffusion Theory, Academic Press, New York, 1968.
R. von Mises and M. Schiffer, On Bergman's integration method in two dimensional compressible fluid flow, Advances in Applied Mechanics, Vol. 1, Academic Press, New York, 1948, 249–285.
P. C. Rosenbloom and D. V. Widder, Expansions in terms of heat polynomials and associated functions, Trans. Amer. Math. Soc. 92 (1959), 220–266.
L. I. Rubinstein, The Stefan Problem. American Mathematical Society, Providence, Rhode Island, 1971.
I. N. Vekua, New Methods for Solving Elliptic Equations, John Wiley, New York, 1967.
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Colton, D. (1974). Integral operators for parabolic equations and their application. In: Colton, D.L., Gilbert, R.P. (eds) Constructive and Computational Methods for Differential and Integral Equations. Lecture Notes in Mathematics, vol 430. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066266
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DOI: https://doi.org/10.1007/BFb0066266
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