Abstract
Unlike ordinary differential equations, where practice and theory seem to be quite compatible, the physical applications of partial differential equations are frequently too idealized to possess solutions. For instance, the theoretical description of the plucked string will not satisfy the partial differential equation from which it came. Although the solution seems to be quite reasonable intuitively, it can not be differentiated often enough to satisfy the idealized wave equation (See Equation XVII.4., no. 2).
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References
A. Friedman, “Generalized Functions and Partial Differential Equations,” Prentice-Hall, Englewood Cliffs, N.J., 1963.
I.M. Gelfand and G.E. Shilov, “Generalized Functions, vol. 1,” Academic Press, New York, 1964.
L. Schwartz, “Theorie des Distributions,” Hermann, Paris, 1966.
I. Stakgold, “Boundary Value Problems of Mathematical Physics, vol. II,” Macmillan, New York, 1968.
A.H. Zemanian, “Distribution Theory and Transform Analysis,” McGraw-Hill, New York, 1965.
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© 1986 D. Reidel Publishing Company, Dordrecht, Holland
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Krall, A.M. (1986). Distributions. In: Applied Analysis. Mathematics and Its Applications, vol 31. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4748-1_14
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DOI: https://doi.org/10.1007/978-94-009-4748-1_14
Publisher Name: Springer, Dordrecht
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