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Integral operators for parabolic equations and their application

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Part of the Lecture Notes in Mathematics book series (LNM,volume 430)

Keywords

  • Integral Operator
  • Parabolic Equation
  • Heat Equation
  • Space Variable
  • Free Boundary Problem

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References

  1. S. Bergman, Integral Operators in the Theory of Linear Partial Differential Equations, Springer-Verlag, Berlin, 1961.

    CrossRef  MATH  Google Scholar 

  2. 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.

    Google Scholar 

  3. S. Bergman, On singularities of solutions of certain differential equations in three variables, Trans. Amer. Math. Soc. 85 (1957), 462–488.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. S. Bergman and M. Schiffer, Kernel Functions and Differential Equations in Mathematical Physics, Academic Press, New York, 1953.

    MATH  Google Scholar 

  5. D. Colton, Integral Operators and reflection principles for parabolic equations in one space variable, J. Diff. Eqns., to appear.

    Google Scholar 

  6. D. Colton, Generalized reflection principles for parabolic equations in one space variable, Duke Math. J., to appear.

    Google Scholar 

  7. D. Colton, The non-characteristic Cauchy problem for parabolic equations in one space variable, SIAM J. Math. Anal., to appear.

    Google Scholar 

  8. D. Colton, The approximation of solutions to initial-boundary value problems for parabolic equations in one space variable, submitted for publication.

    Google Scholar 

  9. A. Friedman, Partial Differential Equations of Parabolic Type, Prentice Hall, Englewood Cliffs, New Jersey, 1964.

    MATH  Google Scholar 

  10. 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.

    Google Scholar 

  11. R. P. Gilbert, Function Theoretic Methods in Partial Differential Equations, Academic Press, New York, 1969.

    MATH  Google Scholar 

  12. R. P. Gilbert, Constructive Methods for Elliptic Partial Differential Equations, Springer-Verlag Lecture Note Series, Berlin, to appear.

    Google Scholar 

  13. C. D. Hill, A method for the construction of reflection laws for a parabolic equation, Trans. Amer. Math. Soc. 20 (1967), 357–372.

    MathSciNet  MATH  Google Scholar 

  14. C. D. Hill, Parabolic equations in one space variable and the non-characteristic Cauchy problem, Comm. Pure. Appl. Math. 20 (1967), 619–633.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. H. Lewy, On the reflection laws of second order differential equations in two independent variables, Bull. Amer. Math. Soc. 65 (1959), 37–58.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. A. V. Luikov, Analytical Heat Diffusion Theory, Academic Press, New York, 1968.

    Google Scholar 

  17. 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.

    Google Scholar 

  18. P. C. Rosenbloom and D. V. Widder, Expansions in terms of heat polynomials and associated functions, Trans. Amer. Math. Soc. 92 (1959), 220–266.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. L. I. Rubinstein, The Stefan Problem. American Mathematical Society, Providence, Rhode Island, 1971.

    Google Scholar 

  20. I. N. Vekua, New Methods for Solving Elliptic Equations, John Wiley, New York, 1967.

    MATH  Google Scholar 

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© 1974 Springer-Verlag

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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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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07021-4

  • Online ISBN: 978-3-540-37302-5

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