Refine your search
Collections
Co-Authors
Journals
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z All
Prasad, Phoolan
- Glimpses of Soliton Theory:The Algebra and Geometry of Nonlinear PDEs, Vol. 54
Abstract Views :233 |
PDF Views:74
Authors
Affiliations
1 Department of Mathematics, Indian Institute of Science, Bengaluru 560 012, IN
1 Department of Mathematics, Indian Institute of Science, Bengaluru 560 012, IN
Source
Current Science, Vol 115, No 12 (2018), Pagination: 2327-2330Abstract
An important revolution took place during the 20th century in two stages in mathematics and physics. This revolution concerns soliton theory.Full Text
- System of kinematical conservation laws
Abstract Views :163 |
PDF Views:72
Authors
Affiliations
1 Department of Mathematics, Indian Institute of Science, Bengaluru 560 012, India, IN
1 Department of Mathematics, Indian Institute of Science, Bengaluru 560 012, India, IN
Source
Current Science, Vol 123, No 12 (2022), Pagination: 1441-1447Abstract
In a wide range of physical phenomena, we find surfaces Wt evolving in time t, which need mathematical treatment. Here, we briefly review the theory of a system of conservation laws known as the kinematical conservation laws (KCLs), which govern the evolution of these surfaces. KCLs are the most general equations in conservation form which govern the evolution of Wt with physically realistic singularities. A special type of singularity is a kink, which is a point on Wt when it is a curve in two dimensions and a curve on Wt when it is a surface in three dimensions. Across a kink, the normal direction n to Wt and the normal velocity m of Wt are discontinuous. This article is aimed at non-experts in the field. Readers may refer to the literature for more detailsKeywords
Curves and surfaces, kinematical conserva-tion laws, kink, ray theory.Full Text
References
- Arun, K. R. and Phoolan Prasad, 3-D kinematical conservation laws (KCL): equations of evolution of a surface. Wave Motion, 2009, 46, 293–311; Preprint available at http://math.iisc.ernet.in/ ~prasad/prasad/preprints/3d_kcl.pdf
- Arun, K. R., A numerical scheme for three-dimensional front prop-agation and control of Jordan mode. SIAM J. Sci. Comput., 2012, 34, B148–B178.
- Arun, K. R. and Phoolan Prasad, Propagation of a three-dimen-sional weak shock front using kinematical conservation laws, 2012, http://math.iisc.ernet.in/~prasad/prasad/preprints/3d_kcl_srt.pdf; 2017 Available on arXiv at: http://arxiv.org/abs/1709.06791
- Arun, K. R. and Phoolan Prasad, System of kinematical conserva-tion laws (KCL): a review article, 2022; https://arxiv.org/pdf/2203.06857.pdf
- Baskar, S. and Phoolan Prasad, Kinematical conservation laws ap-plied to study geometrical shapes of a solitary wave. In Wind Over Waves II: Forecasting and Fundamentals (eds Sajjadi, S. and Hunt, J.), Horwood Publishing Ltd, 2003, pp. 189–200.
- Baskar, S. and Phoolan Prasad, Propagation of curved shock fronts using shock ray theory and comparison with other theories. J. Fluid Mech., 2005, 523, 171–198.
- Courant, R. and Friedrichs, K. O., Supersonic Flow and Shock Saves, Interscience Publishers, New York, USA, 1948.
- Courant, R. and John, F., Introduction to Calculus and Analysis, Vol. II, John Wiley, New York, USA, 1974.
- Lax, P. D., Hyperbolic system of conservation laws II. Commun. Pure Appl. Math., 1957, 10, 537–566.
- Monica, A. and Phoolan Prasad, Propagation of a curved weak shock. J. Fluid Mech., 2001, 434, 119–151.
- Phoolan Prasad and Ravindran, Renuka, Partial Differential Equa-tions, Wiley Eastern Ltd and John Wiley, 1984; https://www.math.iisc.ernet.in/~prasad/prasad/book/PP−RR_PDE_book_1984.pdf
- Phoolan Prasad, Nonlinearity, conservation law and shocks, part I: genuine non-linearity and discontinuous solutions. Resonance, 1997, 2(2), 8–18.
- Phoolan Prasad, Nonlinearity, conservation law and shocks, part II: stability consideration and examples. Resonance, 1997, 2(7), 8–19.
- Phoolan Prasad, Nonlinear hyperbolic waves in multi-dimensions. In Monographs and Surveys in Pure and Applied Mathematics, Chapman and Hall/CRC, 2001, 121.
- Phoolan Prasad, Ray theories for hyperbolic waves, kinematical conservation laws and applications. Indian J. Pure Appl. Math.,2007, 38, 467–490.
- Phoolan Prasad, Kinematical conservation laws in a space of arbi-trary dimensions. Indian J. Pure Appl. Math., 2016, 47(4), 641–653.
- Phoolan Prasad, Propagation of multi-dimensional nonlinear waves and kinematical conservation laws, Springer, Springer Nature Sin-gapore, 2018, doi:10.1007/s12044-016-0275-6. The first 12 pages are available at https://www.math.iisc.ernet.in/~prasad/prasad/book/books.html.
- Sturtevant, B. and Kulkarni, V. A., The focusing of weak shock waves. J. Fluid Mech., 1976, 73, 651–671