|
On the comparison of the spaces  and 
Author(s):
Yudi
Soeharyadi
Journal:
Proc. Amer. Math. Soc.
130
(2002),
405-412.
MSC (2000):
Primary 46B99, 35D10, 47H20, 47D03
Posted:
May 25, 2001
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
The notion of  -variation and the space  arise in the study of regularity properties of solutions to perturbed conservation laws. In this article we show that this notion is equivalent to variation in the regular sense, and therefore the space  is the same as the space  in the sense of Cesari-Tonelli. We also point out some connection between the space  and the Favard classes for translation semigroups.
References:
- 1.
- P. Butzer, H. Berens, Semi-groups of operators and approximation, Springer-Verlag, 1967. MR 37:5588
- 2.
- E. Conway, J. Smoller, Global solutions of the Cauchy problem for quasi-linear first-order equations in several space variables, Comm. Pure Appl. Math. 19 (1966), pp. 95 - 105. MR 33:388
- 3.
- M.G. Crandall, The semigroup approach to first order quasilinear equations in several variables, Israel J. Math. 12 (1972), pp. 108 - 132. MR 47:5473
- 4.
- K.J. Engel, R. Nagel, One parameter semigroups for linear evolution equations, Springer-Verlag, 2000. MR 2000i:47075
- 5.
- L.C. Evans, R.F. Gariepy, Measure Theory and Fine Properties of Functions, CRC Press, 1992. MR 93f:28001
- 6.
- E. Giusti, Minimal surfaces and functions of bounded variation, Birkhauser, 1984. MR 87a:58041
- 7.
- G.R. Goldstein, J.A. Goldstein, S. Oharu, The Favard class for a nonlinear parabolic problem, in Pitman Res. Notes Math. Ser., 324, McBride & Roach (eds), Longman (1995), pp. 134-147. MR 97h:35114
- 8.
- J.A. Goldstein, M.A. Park, Odd solutions to perturbed conservation laws, Bull. Korean Math. Soc. 33 (1996), pp. 521-530. MR 97i:35111
- 9.
- J.A. Goldstein, Y. Soeharyadi, Regularity of solutions to perturbed conservation laws, Appl. Anal. 74 (2000), pp. 185-199. MR 2000j:35175
- 10.
- J.L. Lions, E. Magenes, Non-homogeneous boundary value problems and applications, Vol. I, Springer, 1972. MR 50:2670
- 11.
- R. Nagel, G. Nickel, S. Romanelli, Identification of extrapolation spaces for unbounded operators, Tuebinger Bericht. Funktionalanalysis 3 (1993/1994), pp. 137-152.
- 12.
- D.G. Schaeffer, A regularity theorem for conservation laws, Adv. Math. 11 (1973), pp. 368-386. MR 48:4523
- 13.
- J. Smoller, Shock waves and reaction-diffusion equations, Springer-Verlag, 1994. MR 95g:35002
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
46B99, 35D10, 47H20, 47D03
Retrieve articles in all Journals with MSC
(2000):
46B99, 35D10, 47H20, 47D03
Additional Information:
Yudi
Soeharyadi
Affiliation:
Department of Mathematical Sciences, The University of Memphis, Memphis, Tennessee 38152
Address at time of publication:
Department of Mathematics, Southern Illinois University, Carbondale, Illinois 62901-4408
Email:
ysoehryd@memphis.edu, ysoeharyadi@math.siu.edu
DOI:
10.1090/S0002-9939-01-06044-0
PII:
S 0002-9939(01)06044-0
Keywords:
$L^1$-variation,
variation,
total variation,
essential variation,
conservation laws,
perturbed conservation laws,
$m$-dissipative operator,
invariant set,
Favard class
Received by editor(s):
March 1, 2000
Received by editor(s) in revised form:
June 12, 2000
Posted:
May 25, 2001
Communicated by:
Carmen C. Chicone
Copyright of article:
Copyright
2001,
American Mathematical Society
|
Comments: webmaster@ams.org