Abstract
We consider the way in which a solution to a class of nonlinear partial differential equationsS(u)u t=(K(u)ux)x approaches the similarity form. The problem we solve is chosen for two main reasons: first the equation above is of widespread use in modeling physical situations and second it provides a tractable but significant example of a free boundary problem.
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References
M. L. Storm,J. Appl. Phys. 22:940 (1951).
J. F. Ready,Effects of High Power Laser Radiation (Academic Press, New York, 1971).
A. Munier, J. R. Burgan, J. Gutierrez and E. Fijalkow,SIAM J. Appl. Math. 40: 191 (1984).
R. M. Cherniha and N. D. Cherniha,J. Phys. A: Math. Gen. 26:L935 (1993).
G. W. Bluman and J. D. Cole,Similarity Methods for Differential Equations (Springer, Berlin, 1974).
J. R. Burgan et al.,Group Transformation for Phase Space Fluids in Strongly Coupled Plasma (Plenum Press, New York, 1978).
A. Munier, M. Feix, E. Fijalkow, J. R. Burgan, J. Gutierrez,Astron. Astrophys 78:65 (1979).
R. E. Grundy and R. Mclaughlin,Proc. R. Soc. A 381:395 (1982).
P. J. Olver,Applications of Lie Group's to Differential Equations (Springer, Berlin) (1986).
L. Dresner,Similarity Solutions of Nonlinear Partial Differential Equations (Pitman, London, 1983).
E. A. Saied and S. A. El-wakil,J. Phys. A: Math. Gen. 27:185 (1994).
E. A. Saied and M. H. Magdy,J. Phys. A: Math. Gen. 27:4867 (1994).
E. A. Saied,J. Stat. Phys. 78 (3/4):1139 (1995).
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Saied, E.A. New exact solutions of heat conduction in metals. J Stat Phys 82, 951–962 (1996). https://doi.org/10.1007/BF02179797
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DOI: https://doi.org/10.1007/BF02179797