P. D. Lax, C. S. Morawetz, and R. S. Phillips :
“The exponential decay of solutions of the wave equation in the exterior of a star-shaped obstacle ,”
Bull. Am. Math. Soc.
68 : 6
(1962 ),
pp. 593–595 .
Shorter, early version of an article eventually published in Comm. Pure Appl. Math. 16 :4 (1963) .
MR
142890
Zbl
0108.28301
article

Abstract
People
BibTeX

In this paper we study the behavior for large time of solutions of the wave equation in three space dimensions in the exterior of some smooth, bounded reflecting obstacle which is assumed to be star-shaped. We shall prove that, given an initial disturbance, the bulk of its energy is propagated to infinity.

@article {key142890m,
AUTHOR = {Lax, Peter D. and Morawetz, Cathleen
S. and Phillips, Ralph S.},
TITLE = {The exponential decay of solutions of
the wave equation in the exterior of
a star-shaped obstacle},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {68},
NUMBER = {6},
YEAR = {1962},
PAGES = {593--595},
DOI = {10.1090/S0002-9904-1962-10865-9},
NOTE = {Shorter, early version of an article
eventually published in \textit{Comm.
Pure Appl. Math.} \textbf{16}:4 (1963).
MR:142890. Zbl:0108.28301.},
ISSN = {0002-9904},
}
P. D. Lax, C. S. Morawetz, and R. S. Phillips :
“Exponential decay of solutions of the wave equation in the exterior of a star-shaped obstacle ,”
Comm. Pure Appl. Math.
16 : 4
(November 1963 ),
pp. 477–486 .
A shorter, early version of this article was published in Bull. Am. Math. Soc. 68 :6 (1962) .
MR
155091
Zbl
0161.08001
article

Abstract
People
BibTeX

In this paper we study the behavior for large time of solutions of the wave equation in three space dimensions in the exterior of some smooth, bounded reflecting obstacle, assumed to be star-shaped . We shall prove that, given an initial disturbance, the bulk of its energy is propagated to infinity.

@article {key155091m,
AUTHOR = {Lax, P. D. and Morawetz, C. S. and Phillips,
R. S.},
TITLE = {Exponential decay of solutions of the
wave equation in the exterior of a star-shaped
obstacle},
JOURNAL = {Comm. Pure Appl. Math.},
FJOURNAL = {Communications on Pure and Applied Mathematics},
VOLUME = {16},
NUMBER = {4},
MONTH = {November},
YEAR = {1963},
PAGES = {477--486},
DOI = {10.1002/cpa.3160160407},
NOTE = {A shorter, early version of this article
was published in \textit{Bull. Am. Math.
Soc.} \textbf{68}:6 (1962). MR:155091.
Zbl:0161.08001.},
ISSN = {0010-3640},
}
K. O. Friedrichs :
Selecta ,
vol. 1 .
Edited by C. S. Morawetz .
Contemporary Mathematicians .
Birkhäuser (Boston ),
1986 .
With a foreword by Cathleen S. Morawetz, a biography by Constance Reid, and commentaries by Peter D. Lax, Wolfgang Wasow, Harold Weitzner.
MR
897749
Zbl
0613.01020
book

People
BibTeX
@book {key897749m,
AUTHOR = {Friedrichs, Kurt Otto},
TITLE = {Selecta},
VOLUME = {1},
SERIES = {Contemporary Mathematicians},
PUBLISHER = {Birkh\"auser},
ADDRESS = {Boston},
YEAR = {1986},
PAGES = {427},
NOTE = {Edited by C. S. Morawetz.
With a foreword by Cathleen S. Morawetz,
a biography by Constance Reid, and commentaries
by Peter D. Lax, Wolfgang Wasow, Harold
Weitzner. MR:897749. Zbl:0613.01020.},
ISSN = {0884-7037},
ISBN = {9780817632700},
}
C. S. Morawetz :
“Transonic flow and compensated compactness ,”
pp. 248–258
in
Wave motion: Theory, modelling, and computation
(Berkeley, CA, 9–12 June 1986 ).
Edited by A. J. Chorin and A. J. Majda .
Mathematical Sciences Research Institute Publications 7 .
Springer (New York ),
1987 .
Proceedings of a conference in honor of the 60th birthday of Peter D. Lax.
MR
920838
Zbl
0850.76290
incollection

Abstract
People
BibTeX

The problem of finding steady flow past an airfoil is an old problem going back to the time of Lord Rayleigh. The understanding that there was a difficulty connected to the transition from subsonic flow to supersonic flow must surely, however, be attributed to Chaplygin [1944], whose famous thesis describing solutions of the equations with such transitions was written in 1904. The first mathematical study of such transitions which force a change of type for the differential equations from elliptic to hyperbolic began with the work of Tricomi [1923] in 1923. In 1930 at the International Mechanics Congress, Busemann [1930] with wind tunnel data, and G. I. Taylor [1930] with some computations, presented opposing views of the airfoil problem, the former suggesting that perhaps no steady flow existed and the latter than a series expansion in Mach number gave no evidence of a breakdown when the type changed.

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AUTHOR = {Morawetz, Cathleen S.},
TITLE = {Transonic flow and compensated compactness},
BOOKTITLE = {Wave motion: {T}heory, modelling, and
computation},
EDITOR = {Chorin, Alexandre J. and Majda, Andrew
J.},
SERIES = {Mathematical Sciences Research Institute
Publications},
NUMBER = {7},
PUBLISHER = {Springer},
ADDRESS = {New York},
YEAR = {1987},
PAGES = {248--258},
DOI = {10.1007/978-1-4613-9583-6_9},
NOTE = {(Berkeley, CA, 9--12 June 1986). Proceedings
of a conference in honor of the 60th
birthday of Peter D. Lax. MR:920838.
Zbl:0850.76290.},
ISSN = {0940-4740},
ISBN = {9780387965949},
}
W. Jäger, P. Lax, and C. S. Morawetz :
“Olga Arsen’evna Oleĭnik (1925–2001) ,”
Notices Am. Math. Soc.
50 : 2
(2003 ),
pp. 220–223 .
English version of a Russian language article in Trudy Seminara imeni I. G. Petrovskogo 2003 :23 (2003) . Also published in J. Math. Sci. 120 :3 (2004) .
MR
1951108
Zbl
1159.01335
article

People
BibTeX
@article {key1951108m,
AUTHOR = {J\"ager, Willi and Lax, Peter and Morawetz,
Cathleen Synge},
TITLE = {Olga {A}rsen\cprime evna {O}le\u\i nik
(1925--2001)},
JOURNAL = {Notices Am. Math. Soc.},
FJOURNAL = {Notices of the American Mathematical
Society},
VOLUME = {50},
NUMBER = {2},
YEAR = {2003},
PAGES = {220--223},
URL = {http://www.ams.org/notices/200302/comm-oleinik.pdf},
NOTE = {English version of a Russian language
article in \textit{Trudy Seminara imeni
I. G. Petrovskogo} \textbf{2003}:23
(2003). Also published in \textit{J.
Math. Sci.} \textbf{120}:3 (2004). MR:1951108.
Zbl:1159.01335.},
ISSN = {0002-9920},
}
V. Eger, P. Laks, and K. Moravets :
“Olga Arsen’evna Oleĭnik ,”
Tr. Semin. im. I. G. Petrovskogo
2003 : 23
(2003 ),
pp. 7–15 .
An English version of this article appeared in J. Math. Sci. 120 :3 (2004) and in Notices Am. Math. Soc. 50 :2 (2003) .
MR
2085178
article

People
BibTeX
@article {key2085178m,
AUTHOR = {Eger, V. and Laks, P. and Moravets,
K.},
TITLE = {Olga {A}rsen\cprime evna {O}le\u\i nik},
JOURNAL = {Tr. Semin. im. I. G. Petrovskogo},
FJOURNAL = {Trudy Seminara imeni I. G. Petrovskogo},
VOLUME = {2003},
NUMBER = {23},
YEAR = {2003},
PAGES = {7--15},
NOTE = {An English version of this article appeared
in \textit{J. Math. Sci.} \textbf{120}:3
(2004) and in \textit{Notices Am. Math.
Soc.} \textbf{50}:2 (2003). MR:2085178.},
ISSN = {0321-2971},
}
S. Friedlander, P. Lax, C. Morawetz, L. Nirenberg, G. Seregin, N. Ural’tseva, and M. Vishik :
“Olga Alexandrovna Ladyzhenskaya (1922–2004) ,”
Notices Am. Math. Soc.
51 : 11
(December 2004 ),
pp. 1320–1331 .
MR
2105237
Zbl
1168.01327
article

People
BibTeX
@article {key2105237m,
AUTHOR = {Friedlander, Susan and Lax, Peter and
Morawetz, Cathleen and Nirenberg, Louis
and Seregin, Gregory and Ural\cprime
tseva, Nina and Vishik, Mark},
TITLE = {Olga {A}lexandrovna {L}adyzhenskaya
(1922--2004)},
JOURNAL = {Notices Am. Math. Soc.},
FJOURNAL = {Notices of the American Mathematical
Society},
VOLUME = {51},
NUMBER = {11},
MONTH = {December},
YEAR = {2004},
PAGES = {1320--1331},
URL = {http://www.ams.org/notices/200411/fea-olga.pdf},
NOTE = {MR:2105237. Zbl:1168.01327.},
ISSN = {0002-9920},
}
W. Jäger, P. Lax, and C. S. Morawetz :
“Olga Arsen’evna Oleinik ,”
J. Math. Sci.
120 : 3
(2004 ),
pp. 1242–1246 .
English version of a Russian language article in Tr. Semin. im. I. G. Petrovskogo 2003 :23 (2003) . Also published in Notices Am. Math. Soc. 50 :2 (2003) .
Zbl
1077.01014
article

People
BibTeX
@article {key1077.01014z,
AUTHOR = {J\"ager, W. and Lax, P. and Morawetz,
C. S.},
TITLE = {Olga {A}rsen\cprime evna {O}leinik},
JOURNAL = {J. Math. Sci.},
FJOURNAL = {Journal of Mathematical Sciences,},
VOLUME = {120},
NUMBER = {3},
YEAR = {2004},
PAGES = {1242--1246},
DOI = {10.1023/B:JOTH.0000016046.59508.ff},
NOTE = {English version of a Russian language
article in \textit{Tr. Semin. im. I.
G. Petrovskogo} \textbf{2003}:23 (2003).
Also published in \textit{Notices Am.
Math. Soc.} \textbf{50}:2 (2003). Zbl:1077.01014.},
ISSN = {1072-3374},
}