By Robert A. Kowalski
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Nauk SSSR 13, 475 (1950). 7. , Some considerations on thermal conduction and magnetic fields in prominences, in “Electromagnetic Phenomena in Cosmical Physics” (B. ), p. 150. Cambridge Univ. Press, London and New York, 1958. 8. Hirschfelder, J. , Curtiss, C. , and Bird, R. ” Wiley, New York, 1954. 18 1. ORIGIN OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS 9. Spitzer, J. ” Wiley (Interscience), New York, 1956. 10. Pai, S. ” Springer, Vienna (Prentice-Hall, Englewood Cliffs, New Jersey), 1962. 11. , and Friedrichs, K.
160) F’ + G x ” = FGp(p - ~ ) x P - * + G2p(2p- 1)~”-’ with unknowns F and G. 162) then F may be determined from F' -- 2FG = 0. 163) Performing these integrations we find that with C and D as constants to be determined from stated auxiliary conditions. It is immediately obvious from these results that such solutions have limited utility but indicate a direction of attack. Last, if one attempts to find a solution of the form w = F(t) H(x), except for the trivial solution x t when n = 1, it is seen to be not possible.
22. Katz, S. , Kuba, E. , and Wakelin, J. , The chemical attack on polymeric materials as modified by diffusion, Textile Res. J . 20, 754 (1950). 23. Reese, C. , Mechanical properties and the structure of hair, Textile Res. J. 20, 743 (1950). 24. , and Nicolson. , A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type, Proc. Cambridge Phil. 43, 50 (1947). 25. Jones, B. , The determination of a coefficient in a parabolic differential equation, Part I.