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A new type of boundary-value problem in hyperbolic equations

Published online by Cambridge University Press:  24 October 2008

S. Chandrasekhar
S. Chandrasekhar
Affiliation:
Yerkes ObservatoryWilliams Bay, Wisconsin
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Extract

In developing the theory of radiative transfer in expanding atmospheres (Chandrasekhar, 1945 a, b) the author has recently encountered certain novel types of boundary-value problems in hyperbolic equations which appear to merit consideration for their own sake. As related to the equation

the boundary-value problems which occur are of the following general type

i.e. along AB in Fig. 1. Along AD (x = 0 and 0 ≤ y ≤ l2) and BC (x = l1, 0 ≤ y ≤ l2) we are further given that

and

where φ(y) and ψ(y) are two known functions. The problem is to solve equation (1) in the rectangular strip ABCD satisfying the stated boundary conditions.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 42 , Issue 3 , October 1946 , pp. 250 - 260
Copyright
Copyright © Cambridge Philosophical Society 1946

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References

REFERENCES

Chandrasekhar, S.Rev. Mod. Phys.. 17 (1945 a), 138.CrossRefGoogle Scholar
Chandrasekhar, S.Astrophys. J.. 102 (1945 b), 402.CrossRefGoogle Scholar
Frank, P. and von Mises, R.Die Differential Gleichungen der Mechanik und Physik (New York: Rosenberg (1943)), pp. 779–817.Google Scholar
Wesster, A. G.Partial Differential Equations of Mathematical Physics (New York: Stechert (1933)), pp. 160–88.Google Scholar