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Existence Theorem for the Initial-Boundary Value Problem for a Singular Parabolic Partial Differential Equation

Published online by Cambridge University Press:  20 November 2018

Julius A. Krantzberg
Julius A. Krantzberg*
Affiliation:
Loyola College, Montreal, Quebec
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We consider the initial-boundary value problem for the parabolic partial differential equation

1.1

in the bounded domain D, contained in the upper half of the xy-plane, where a part of the x-axis lies on the boundary B(see Fig.1).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 2 , June 1972 , pp. 229 - 234
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Courant, R. and Hilbert, D., Methods of mathematical physics II, Interscience, New York, (1962), 261-264.Google Scholar
2. Garabedian, P. R., Partial differential equations, Wiley, New York, (1964), 492-499.Google Scholar
3. Huber, A., On the uniqueness of generalized axially symmetric potentials, Ann. of Math. 60 (1954), 351-358.Google Scholar
4. Jamet, P., Numerical methods and existence theorems for parabolic differential equations whose coefficients are singular on the boundary. Math. Comp. 22 (1968), 721-743.Google Scholar
5. Jamet, P. and Parter, S. V., Numerical methods for elliptic differential equations whose coefficients are singular on a portion of the boundary. SIAM J. Numer. Anal. 4 (1967), 131-146.Google Scholar
6. Rothe, E., Zweidimensionale Parabolische Randwert-aufgaben als Grenzfall Eindimentionaler Randwert-aufgaben. Math. Ann. 102 (1930), 650-670.Google Scholar
7. Rothe, E., Über die Wä;rmeleitungsgleichung mit nichtkonstaten Koeffizientem im rdumlichen Falle. Math. Ann. 104 (1931), 340-354.Google Scholar
8. Rubinstein, Z., A course in ordinary and partial differential equations. Academic Press, New York, (1969), 361-369.Google Scholar
9. Schechter, M., On the Dirichlet problem for second order elliptic equations with coefficients singular at the boundary. Comm. Pure Appl. Math. 13 (1960), 321-328.Google Scholar
10. Weinacht, R. J., Fundamental solutions for the class of singular equations. Contributions to Differential Equations, 3 (1964), 43-55.Google Scholar
11. Weinstein, A., Generalized axially symmetric potential theory. Bull. Amer. Math. Soc. 59 (1953), 20-38.Google Scholar
12. Weinstein, A., Discontinuous integrals and generalized potential theory, Trans. Amer. Math. Soc. 63, (1948), 342-354.Google Scholar