The Cauchy problem for a class of quasilinear parabolic equations

Annali di Matematica Pura ed Applicata

Volumn 182, Issue 3, 2003, Pages 325-336

  Tersenov, Alkis S ^a   Tersenov, Aris S ^b  

^a UNIVERSITY OF CRETE   (Greece)

^b INSTITUTE OF COMPUTER SCIENCE   (Greece)

Author keywords

Hamilton Jacobi equation; Quasilinear parabolic equations

Indexed keywords

EID: 2942519540     PISSN: 03733114     EISSN: 16181891     Source Type: Journal    
DOI: 10.1007/s10231-002-0070-0     Document Type: Article

References (18)

1. Barles, G.: Uniqueness and regularity results for first order Hamilton-Jacobi equations. Indiana Univ. Math. J. 39, 443-466 (1990)
2. Crandall, M.G., Lions, P.L.: Viscosity solutions of Hamilton-Jacobi equations. Trans. Am. Math. Soc. 277, 1-42 (1983)
3. Gilbarg, D., Trudinger, N.S.: Elliptic Partial Differential Equations of Second Order (2nd ed.). Springer 1983
4. Kamynin, V.L.: Apriori estimates for solutions of quasilinear parabolic equations in the plane and their applications. Differ. Equations 19, 590-598 (1983)
5. Khusnutdinova, N.V.: On condition for the boundedness of the gradient of the solution of degenerated parabolic equation. Din. Splosh. Sredy 72, 120-129 (1985) (Russian)
6. Kondrat'ev, V.A., Oleinik, O.A.: Boundary value problems for partial differential equations in nonsmooth domains. Usp. Mat. Nauk 38, 3-76 (1983) (Russian)
7. Kruzhkov, S.N.: Nonlinear parabolic equations in two independent variables. Trans. Mosc. Math. Soc. 16, 355-373 (1968)
8. Kruzhkov, S.N.: Quasilinear parabolic equations and systems with two independent variables. Trudy Sem. Petrovsk. Vyp. 5, 217-272 (1979) (Russian).
9. English transi, in Topics in Modern Math., Consultants Bureau, New York 1985
10. Ladyzhenskaja, O.A., Solonnikov, V.A., Urarceva, N.N.:Linearand Quasilinear Equations of Parabolic Type. Amer. Math. Soc. Transl. (2), Vol. 23 (1968)
11. Lieberman, G.M.: Second Order Parabolic Equations. River Edge, NJ: World Scientific Publishing Co., Inc. 1996
12. Lions, P.L.: Generalized solutions of Hamilton-Jacobi equations. Boston: Pitman 1982
13. Nazarov, S., Plamenevskii, B.: Elliptic problems in domains with piecewise smooth boundaries, de Gruyter Expositions in Mathematics, 13. Berlin: Walter de Gruyter and Co. 1994
14. Tersenov, Al.S.: On quasilinear non-uniformly parabolic equations in general form. J. Diff. Equations 142, 263-276 (1998)
15. Tersenov, Al.S.: On the first boundary value problem for quasilinear parabolic equations with two independent variables. Arch. Ration. Mech. Anal. 152, 81-92 (2000)
16. Tersenov, Al.S., Tersenov, Ar.S.: Global solvability for a class of quasilinear parabolic equations. Indiana Univ. Math. J. 50, 1899-1913 (2001)
17. Tersenov Ar.S.: A remark on the global solvability of the Cauchy problem for quasilinear parabolic equations. J. Math. Anal. Appl. 260, 46-54 (2001)
18. Van, T.D., Hoang, N., Tsuji, M.: On Hopf's formula for Lipschitz solutions of the Cauchy problem for Hamilton-Jacobi equations. Nonlinear Anal. 29, 1145-1159 (1997)