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By Siddiqi A.H., et al. (eds.)

ISBN-10: 9814338818

ISBN-13: 9789814338813

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Maslov, J. Sov. Math. 13, 119 (1980). 19. R. Ravindran and P. Prasad, Appl. Math. Lett. 3, 77 (1990). 20. S. Baskar and P. Prasad, Proc. Indian Acad. Sci. Math. Sci. 116, 97 (2006). 21. P. Prasad, Indian J. Pure Appl. Math. 38, 467 (2007). 22. M. B. Giles, P. Prasad and R. indd 43 6/8/11 7:33 PM 23. 24. 25. 26. 27. 28. 29. three dimensional front propagation, tech. , Department of Mathematics, Indian Institute of Science (Bangalore, 1995). R. Courant and F. John, Introduction to Calculus and Analysis (John Wiley and Sons, New York, 1974).

We assume for the derivation of KCL that this gives a mapping: (ξ, t) → (x1 , x2 ) which is smooth. e. u = (−n2 , n1 ). Equating (x1 )ξt = (x1 )tξ and (x2 )ξt = (x2 )tξ , we get the 2-D KCLb (gn1 )t − (mn2 )ξ = 0. (gn2 )t + (mn1 )ξ = 0, (4) From the conservation laws (4), we can derive the jump relations across a shock ξ = ξs (t) in (ξ, t)-plane. This leads to the shock velocity K = dξs /dt as K=± m2− − m2+ 2 − g2 g+ − 1/2 , (5) where the symbols + and − refer to the states on the two sides. Fig.

19, 2003, pp. 355–372. 4. D. Han, M. Z. Nashed, and Q. Sun, Sampling expansions in reproducing kernel Hilbert and Banach spaces, Numerical Functional Analysis and Optimization, Vol. 30, 2009, pp. 971–987. 5. M. Z. Nashed, Applications of wavelets and kernel methods in inverse problems, In Integral Methods in Science and Engineering Theoretical and Practical Aspects, C. Constanda, Z. Nashed, and D. Rollins eds, Birkhuser, 2006, pp. 189-197. 6. M. Z. Nashed and Q. Sun, Sampling and reconstruction of signals in a reproducing kernel subspace of Lp (Rd ), J.

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