Existence Theorem for the Initial-Boundary Value Problem for a Singular Parabolic Partial Differential Equation
Canadian mathematical bulletin, Tome 15 (1972) no. 2, pp. 229-234

Voir la notice de l'article provenant de la source Cambridge University Press

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).
Krantzberg, Julius A. Existence Theorem for the Initial-Boundary Value Problem for a Singular Parabolic Partial Differential Equation. Canadian mathematical bulletin, Tome 15 (1972) no. 2, pp. 229-234. doi: 10.4153/CMB-1972-042-2
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[1] 1. Courant, R. and Hilbert, D., Methods of mathematical physics II, Interscience, New York, (1962), 261-264. Google Scholar

[2] 2. Garabedian, P. R., Partial differential equations, Wiley, New York, (1964), 492-499. Google Scholar

[3] 3. Huber, A., On the uniqueness of generalized axially symmetric potentials, Ann. of Math. 60 (1954), 351-358. Google Scholar

[4] 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] 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] 6. Rothe, E., Zweidimensionale Parabolische Randwert-aufgaben als Grenzfall Eindimentionaler Randwert-aufgaben. Math. Ann. 102 (1930), 650-670. Google Scholar

[7] 7. Rothe, E., Über die Wä;rmeleitungsgleichung mit nichtkonstaten Koeffizientem im rdumlichen Falle. Math. Ann. 104 (1931), 340-354. Google Scholar

[8] 8. Rubinstein, Z., A course in ordinary and partial differential equations. Academic Press, New York, (1969), 361-369. Google Scholar

[9] 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] 10. Weinacht, R. J., Fundamental solutions for the class of singular equations. Contributions to Differential Equations, 3 (1964), 43-55. Google Scholar

[11] 11. Weinstein, A., Generalized axially symmetric potential theory. Bull. Amer. Math. Soc. 59 (1953), 20-38. Google Scholar

[12] 12. Weinstein, A., Discontinuous integrals and generalized potential theory, Trans. Amer. Math. Soc. 63, (1948), 342-354. Google Scholar

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