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The Cauchy Problem For Linear Partial Differential Equations With Restricted Boundary Conditions

Published online by Cambridge University Press:  20 November 2018

E. P. Miles Jr.  and
Ernest Williams
E. P. Miles Jr.
Affiliation:
Alabama Polytechnic Institute, Auburn, Alabama
Ernest Williams
Affiliation:
Alabama Polytechnic Institute, Auburn, Alabama
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We shall discuss solutions of linear partial differential equations of the form

1

where Ψ is an ordinary differential operator of order s with respect to t. Our first theorem gives a solution of (1) for the Cauchy data;

2

j = 1,2, ߪ,s − 1,

whenever the function P is annihilated by a finite iteration of the operator Φ.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 426 - 431
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Miles, E. P., Jr. and Williams, Ernest, A basic set of homogeneous harmonic polynomials in k variables, Proc. Amer. Math. Soc, 6 (1955), 191–194.Google Scholar
2. Miles, E. P., Jr., A basic set of polynomial solutions for the Euler-Poisson-Darboux and Beltrami equations. To appear in the American Mathematical Monthly.Google Scholar
3. Weinstein, Alexander, On the wave equation and the equation of Euler-Poisson, Proc. Fifth Symposium in Applied Mathematics (New York, 1954), 137–147.Google Scholar