A new PDE approach to the large time asymptotics of solutions of Hamilton–Jacobi equations

Guy Barles1,2, Hitoshi Ishii3,4, Hiroyoshi Mitake5
1Fédération de recherche Denis Poisson
2Laboratoire de Mathématiques et Physique Théorique
3Department of Mathematics
4Mathematics Department
5Department of Applied Mathematics

Tóm tắt

Từ khóa


Tài liệu tham khảo

Barles, G.: Remarques sur des résultats d’existence pour les équations de Hamilton–Jacobi du premier ordre. Ann. Inst. H. Poincaré Anal. Non Linéaire 2(1), 21–32 (1985)

Barles, G.: Solutions de viscosité des équations de Hamilton–Jacobi, Math. Appl. (Berlin), 17. Springer, Paris (1994)

Barles, G., Ishii, H., Mitake, H.: On the large time behavior of solutions of Hamilton–Jacobi equations associated with nonlinear boundary conditions. Arch. Ration. Mech. Anal. 204(2), 515–558 (2012)

Barles, G., Mitake, H.: A PDE approach to large-time asymptotics for boundary-value problems for nonconvex Hamilton–Jacobi equations. Commun. Partial Differ. Equ. 37(1), 136–168 (2012)

Barles, G., Souganidis, P.E.: On the large time behavior of solutions of Hamilton–Jacobi equations. SIAM J. Math. Anal. 31(4), 925–939 (2000)

Cagnetti, F., Gomes, D.A., Mitake, H., Tran, H.V.: A new method for large time behavior of convex Hamilton–Jacobi equations I: degenerate equations and weakly coupled systems, submitted (arXiv: 1212.4694)

Crandall, M.G., Ishii, H., Lions, P.-L.: User’s guide to viscosity solutions of second order partial differential equations. Bull. Am. Math. Soc. (N.S.) 27(1), 1–67 (1992)

Davini, A., Siconolfi, A.: A generalized dynamical approach to the large time behavior of solutions of Hamilton–Jacobi equations. SIAM J. Math. Anal. 38(2), 478–502 (2006)

Fathi, A.: Sur la convergence du semi-groupe de Lax-Oleinik. C. R. Acad. Sci. Paris Sér. I Math. 327(3), 267–270 (1998)

Fujita, Y., Ishii, H., Loreti, P.: Asymptotic solutions of Hamilton–Jacobi equations in Euclidean $$n$$ space. Indiana Univ. Math. J. 55(5), 1671–1700 (2006)

Ichihara, N., Ishii, H.: The large-time behavior of solutions of Hamilton–Jacobi equations on the real line. Methods Appl. Anal. 15(2), 223–242 (2008)

Ichihara, N., Ishii, H.: Long-time behavior of solutions of Hamilton–Jacobi equations with convex and coercive Hamiltonians. Arch. Ration. Mech. Anal. 194(2), 383–419 (2009)

Ishii, H.: A simple, direct proof of uniqueness for solutions of the Hamilton–Jacobi equations of eikonal type. Proc. Am. Math. Soc. 100(2), 247–251 (1987)

Ishii, H.: Asymptotic solutions for large time of Hamilton–Jacobi equations in Euclidean $$n$$ space. Ann. Inst. H. Poincaré Anal. Non Linéaire 25(2), 231–266 (2008)

Ishii, H.: Long-time asymptotic solutions of convex Hamilton–Jacobi equations with Neumann type boundary conditions. Calc. Var. Partial Differ. Equ. 42(1–2), 189–209 (2011)

Lions, P.-L., Papanicolaou, G., Varadhan, S.R.S.: Homogenization of Hamilton–Jacobi equations. Unpublished work

Mitake, H.: Asymptotic solutions of Hamilton–Jacobi equations with state constraints. Appl. Math. Optim. 58(3), 393–410 (2008)

Mitake, H.: The large-time behavior of solutions of the Cauchy–Dirichlet problem for Hamilton–Jacobi equations. NoDEA Nonlinear Differ. Equ. Appl. 15(3), 347–362 (2008)

Namah, G., Roquejoffre, J.-M.: Remarks on the long time behaviour of the solutions of Hamilton–Jacobi equations. Commun. Partial Differ. Equ. 24(5–6), 883–893 (1999)