Fractal first-order partial differential equations

Archive for Rational Mechanics and Analysis

Volumn 182, Issue 2, 2006, Pages 299-331

  Droniou, Jérôme ^a   Imbert, Cyril ^a,b  

^a UNIVERSITÉ DE MONTPELLIER   (France)

^b UNIV MONTPELLIER   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33747469213     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-006-0429-2     Document Type: Article

References (26)

1. ALVAREZ, O., TOURIN, A.: Viscosity solutions of nonlinear integro-differential equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 13, 293-317 (1996)
2. BARLES, G.: Solutions de viscosité des équations de Hamilton-Jacobi, Mathématiques et applications. Springer-Verlag, Berlin, 1994
3. BILER, P., FUNAKI, T., WOYCZYNSKI, W.: Fractal Burgers Equations. J. Differential Equations 148, 9-46 (1998)
4. BILER, P., KARCH, G., WOYCZYNSKI, W.: Asymptotics for multifractal conservation laws. Studia Math. 135, 231-252 (1999)
5. BENTH, F.E., KARLSEN, K.H., REIKVAM, K.: Optimal portfolio selection with consumption and nonlinear integro-differential equations with gradient constraint: a viscosity solution approach. Finance Stoch. 5, 275-303 (2001)
6. BENTH, F.E., KARLSEN, K.H., REIKVAM, K.: Optimal portfolio management rules in a non-Gaussian market with durability and inteitemporal substitution. Finance Stoch. 5, 447-467 (2001)
7. BENTH, F.E., KARLSEN, K.H., REIKVAM, K.: Portfolio optimization in a Lévy market with intertemporal substitution and transaction costs. Stoch. Stoch. Rep. 74, 517-569 (2002)
8. CLAVIN, P.: Instabilities and nonlinear patterns of overdriven detonations in gases. Nonlinear PDE's in Condensed Matter and Reactive Flows (Eds. BERESTYCKI, H., POMEAU, Y.), Kluwer, pp. 49-97, 2002
9. CLARKE, F.H., LEDYAEV, Yu.S., STERN, R.J., WOLENSKI, P.R.: Nonsmooth analysis and control theory. Graduate Texts in Mathematics, 178, Springer, Berlin, 1997
10. CÓRDOBA, A., CÓRDOBA, D.: A maximum principle applied to quasi-geostrophic equations. Comm. Math. Phys. 249, 511-528 (2004)
11. CRANDALL, M.G., ISHII, H., LIONS, P.-L.: User's guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. (N.S.) 27, 1-67 (1992)
12. DRONIOU, J.: Vanishing non-local regularization of a scalar conservation law. Electron. J. Differential Equations 2003, 1-20 (2003)
13. DRONIOU, J.: Etude théorique et numérique d'équations aux dérivées partielles elliptiques, paraboliques et non-locales. Mémoire d'Habilitation à Diriger les Recherches, Université Montpellier II, France. Available at http:// www-gm3.univ-mrs.fr/~droniou/travaux-en.html
14. DRONIOU, J., GALLOUËT, T., VOVELLE, J.: Global solution and smoothing effect for a non-local regularization of an hyperbolic equation. J. Evol. Equ. 3, 499-521 (2003)
15. FRIEDMAN, A.: Partial Differential Equations of Parabolic Type. Prentice-Hall, Inc., Englewood Cliffs, NJ, 1964
16. GARRONI, M.G., MENALDI, J.L.: Green functions for second order parabolic integrodifferential problems. Longman Scientific and Technical, Burnt Mill, Harlow, 1992
17. IMBERT, C.: A non-local reguralization of first order Hamilton-Jacobi equations. J. Differential Equations, 211, 214-246 (2005)
18. JAKOBSEN, E.R., KARLSEN, K.H.: Continuous dependence estimates for viscosity solutions of integro-fs. Preprint
19. JAKOBSEN, E.R., KARLSEN, K.H.: A maximum principle for semicontinuous functions applicable to integro-partial differential equations. Preprint
20. KRUSHKOV, S.N.: First Order quasilinear equations with several space variables. Math. USSR. Sb. 10, 217-243 (1970)
21. KUZNECOV, N.N.: The accuracy of certain approximate methods for the computation of weak solutions of a first order quasilinear equation. Ž. Vyčisl. Mat. i Mat. Fiz. 16, 1489-1502 (1976)
22. SAYAH, A.: Équations d'Hamilton-Jacobi du premier ordre avec termes intégro-différentiels. I. Unicité des solutions de viscosité, II. Existence de solutions de viscosité. Comm. Partial Differential Equations 16, 1057-1093 (1991)
23. SONER, H.M.: Optimal control with state-space constraint. II. SIAM J. Control Optim. 24, 1110-1122 (1986)
24. SONER, H.M.: Optimal control of jump-Markov processes and viscosity solutions. Stochastic Differential Systems, Stochastic Control Theory and Applications. The IMA Volumes in Mathematics and its Applications, 10, Springer, New York, pp. 501-511, 1988
25. TAYLOR, M.E.: Partial Differential Equations III (nonlinear equations). Applied Mathematical Sciences 117, Springer-Verlag, New York, 1997
26. WOYCZYŃSKI, W.A.: Lévy processes in the physical sciences. Lévy Processes, pp. 241-266, Birkhäuser Boston, Boston, MA, 2001