On the vanishing viscosity method for first order differential-functional IBVP
Czechoslovak Mathematical Journal (2008)
- Volume: 58, Issue: 4, page 927-947
- ISSN: 0011-4642
Access Full Article
topAbstract
topHow to cite
topTopolski, Krzysztof A.. "On the vanishing viscosity method for first order differential-functional IBVP." Czechoslovak Mathematical Journal 58.4 (2008): 927-947. <http://eudml.org/doc/37878>.
@article{Topolski2008,
abstract = {We consider the initial-boundary value problem for first order differential-functional equations. We present the `vanishing viscosity' method in order to obtain viscosity solutions. Our formulation includes problems with a retarded and deviated argument and differential-integral equations.},
author = {Topolski, Krzysztof A.},
journal = {Czechoslovak Mathematical Journal},
keywords = {viscosity solutions; first order equation; parabolic equation; differential functional equations; viscosity solutions; first order equation; parabolic equation; differential functional equations},
language = {eng},
number = {4},
pages = {927-947},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the vanishing viscosity method for first order differential-functional IBVP},
url = {http://eudml.org/doc/37878},
volume = {58},
year = {2008},
}
TY - JOUR
AU - Topolski, Krzysztof A.
TI - On the vanishing viscosity method for first order differential-functional IBVP
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 4
SP - 927
EP - 947
AB - We consider the initial-boundary value problem for first order differential-functional equations. We present the `vanishing viscosity' method in order to obtain viscosity solutions. Our formulation includes problems with a retarded and deviated argument and differential-integral equations.
LA - eng
KW - viscosity solutions; first order equation; parabolic equation; differential functional equations; viscosity solutions; first order equation; parabolic equation; differential functional equations
UR - http://eudml.org/doc/37878
ER -
References
top- Alvarez, O., Tourin, A., 10.1016/S0294-1449(16)30106-8, Ann. Inst. H. Poincaré anal. Non Linaire 13 (1996), 293-317. (1996) Zbl0870.45002MR1395674DOI10.1016/S0294-1449(16)30106-8
- Bardi, M., Crandall, M. G., Evans, L. C., Soner, H. M., Souganidis, P. E., Viscosity Solutions and Applications, Springer-Verlag Berlin-Heidelberg-New York (1997). (1997)
- Brandi, P., Ceppitelli, R., On the existance of solutions of nonlinear functional partial differential equations of the first order, Atti Sem. Mat. Fis. Univ. Modena 29 (1980), 166-186. (1980) MR0632726
- Brandi, P., Ceppitelli, R., 10.4064/ap-47-2-121-136, Ann. Polon. Math. 47 (1986), 121-136. (1986) Zbl0657.35124MR0884930DOI10.4064/ap-47-2-121-136
- Brzychczy, S., Chaplygin's method for a system of nonlinear parabolic differential-functional equations, Differen. Urav. 22 (1986), 705-708 Russian. (1986) MR0843232
- Brzychczy, S., 10.4064/ap-47-3-309-317, Ann. Polon. Math. 47 (1987), 309-317. (1987) MR0927579DOI10.4064/ap-47-3-309-317
- Crandall, M. G., Ishii, H., Lions, P. L., 10.1090/S0273-0979-1992-00266-5, Bull. Amer. Math. Soc. 27 (1992), 1-67. (1992) Zbl0755.35015MR1118699DOI10.1090/S0273-0979-1992-00266-5
- Crandall, M. G., Lions, P. L., 10.1090/S0002-9947-1983-0690039-8, Trans. Amer. Math. Soc. 277 (1983), 1-42. (1983) Zbl0599.35024MR0690039DOI10.1090/S0002-9947-1983-0690039-8
- Hale, J. K., Lunel, S. M. V., Introduction to Functional Differential Equations, Springer-Verlag New York (1993). (1993) Zbl0787.34002MR1243878
- Ishii, H., Koike, S., Viscosity solutions of functional differential equations, Adv. Math. Sci. Appl. Gakkotosho, Tokyo 3 (1993/94), 191-218. (1993) MR1287929
- Jakobsen, E. R., Karlsen, K. H., 10.1016/j.jde.2004.06.021, J. Differential Equations 212 (2005), 278-318. (2005) MR2129093DOI10.1016/j.jde.2004.06.021
- Kamont, Z., Initial value problems for hyperbolic differential-functional systems, Boll. Un. Mat. Ital. 171 (1994), 965-984. (1994) Zbl0832.35144MR1315829
- Kruzkov, S. N., Generalized solutions of first order nonlinear equations in several independent variables I, Mat. Sb. 70 (1966), 394-415 II, Mat.Sb. (N.S) 72 (1967), 93-116 Russian. (1967) MR0199543
- Ladyzhenskaya, O. A., Solonikov, V. A., Uralceva, N. N., Linear and Quasilinear Equations of Parabolic Type, Nauka, Moskva (1967), Russian Translation of Mathematical Monographs, Vol. 23, Am. Math. Soc., Providence, R.I. (1968). (1968) MR0241822
- Lions, P. L., Generalized Solutions of Hamilton-Jacobi Equations, Pitman, London (1982). (1982) Zbl0497.35001MR0667669
- Sayah, A., 10.1080/03605309108820789, Comm. Partial Differential Equations 16 (1991), 1057-1093. (1991) MR1116853DOI10.1080/03605309108820789
- Topolski, K., 10.4064/ap-59-1-65-75, Ann. Polon. Math. 59 (1994), 65-75. (1994) Zbl0804.35138MR1270302DOI10.4064/ap-59-1-65-75
- Topolski, K., 10.4064/ap-68-1-17-25, Ann. Polon. Math. 68 (1998), 17-25. (1998) MR1606607DOI10.4064/ap-68-1-17-25
- Topolski, K. A., 10.1155/S1085337598000608, Abstr. Appl. Anal. 3 (1998), 363-375. (1998) MR1749416DOI10.1155/S1085337598000608
- Topolski, K. A., On the existence of viscosity solutions for the differential-functional Cauchy problem, Comment. Math. 39 (1999), 207-223. (1999) Zbl0972.35173MR1739030
- Topolski, Krzysztof A., On the existence of viscosity solution for the parabolic differential-functional Cauchy problem, Preprint.
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.