Giga, Yoshikazu; Mitake, Hiroyoshi; Tran, Hung V. Remarks on large time behavior of level-set mean curvature flow equations with driving and source terms. (English) Zbl 07272910 Discrete Contin. Dyn. Syst., Ser. B 25, No. 10, 3983-3999 (2020). MSC: 35B40 35K93 35K20 53E10 PDF BibTeX XML Cite \textit{Y. Giga} et al., Discrete Contin. Dyn. Syst., Ser. B 25, No. 10, 3983--3999 (2020; Zbl 07272910) Full Text: DOI
Jing, Wenjia; Mitake, Hiroyoshi; Tran, Hung V. Generalized ergodic problems: existence and uniqueness structures of solutions. (English) Zbl 1430.35052 J. Differ. Equations 268, No. 6, 2886-2909 (2020). MSC: 35F21 35B10 35B27 35B40 35D40 49L25 PDF BibTeX XML Cite \textit{W. Jing} et al., J. Differ. Equations 268, No. 6, 2886--2909 (2020; Zbl 1430.35052) Full Text: DOI arXiv
Mitake, Hiroyoshi; Tran, Hung V.; Yu, Yifeng Rate of convergence in periodic homogenization of Hamilton-Jacobi equations: the convex setting. (English) Zbl 1416.35034 Arch. Ration. Mech. Anal. 233, No. 2, 901-934 (2019). Reviewer: Paolo Musolino (Padova) MSC: 35B27 35F21 35B40 PDF BibTeX XML Cite \textit{H. Mitake} et al., Arch. Ration. Mech. Anal. 233, No. 2, 901--934 (2019; Zbl 1416.35034) Full Text: DOI arXiv
Mitake, Hiroyoshi; Tran, Hung V. On uniqueness sets of additive eigenvalue problems and applications. (English) Zbl 1401.37069 Proc. Am. Math. Soc. 146, No. 11, 4813-4822 (2018). Reviewer: Stepan Agop Tersian (Rousse) MSC: 37J50 49L25 35B40 PDF BibTeX XML Cite \textit{H. Mitake} and \textit{H. V. Tran}, Proc. Am. Math. Soc. 146, No. 11, 4813--4822 (2018; Zbl 1401.37069) Full Text: DOI arXiv
Gomes, Diogo A.; Mitake, Hiroyoshi; Tran, Hung V. The selection problem for discounted Hamilton-Jacobi equations: some non-convex cases. (English) Zbl 1403.35082 J. Math. Soc. Japan 70, No. 1, 345-364 (2018). MSC: 35F21 35B40 37J50 49L25 PDF BibTeX XML Cite \textit{D. A. Gomes} et al., J. Math. Soc. Japan 70, No. 1, 345--364 (2018; Zbl 1403.35082) Full Text: DOI arXiv
Le, Nam Q.; Mitake, Hiroyoshi; Tran, Hung V. Appendix of Part II. (English) Zbl 1373.35003 Mitake, Hiroyoshi (ed.) et al., Dynamical and geometric aspects of Hamilton-Jacobi and linearized Monge-Ampére equations. VIASM 2016. Based on lectures at the Rutgers University, NJ, USA, 2013. Cham: Springer (ISBN 978-3-319-54207-2/pbk; 978-3-319-54208-9/ebook). Lecture Notes in Mathematics 2183, 207-228 (2017). MSC: 35-02 35D40 35F21 PDF BibTeX XML Cite \textit{N. Q. Le} et al., Lect. Notes Math. 2183, 207--228 (2017; Zbl 1373.35003) Full Text: DOI
Le, Nam Q.; Mitake, Hiroyoshi; Tran, Hung V. Selection problems in the discounted approximation procedure. (English) Zbl 1373.35002 Mitake, Hiroyoshi (ed.) et al., Dynamical and geometric aspects of Hamilton-Jacobi and linearized Monge-Ampére equations. VIASM 2016. Based on lectures at the Rutgers University, NJ, USA, 2013. Cham: Springer (ISBN 978-3-319-54207-2/pbk; 978-3-319-54208-9/ebook). Lecture Notes in Mathematics 2183, 177-206 (2017). MSC: 35-02 35J62 35D40 PDF BibTeX XML Cite \textit{N. Q. Le} et al., Lect. Notes Math. 2183, 177--206 (2017; Zbl 1373.35002) Full Text: DOI
Le, Nam Q.; Mitake, Hiroyoshi; Tran, Hung V. Large time asymptotics of Hamilton-Jacobi equations. (English) Zbl 1382.35040 Mitake, Hiroyoshi (ed.) et al., Dynamical and geometric aspects of Hamilton-Jacobi and linearized Monge-Ampére equations. VIASM 2016. Based on lectures at the Rutgers University, NJ, USA, 2013. Cham: Springer (ISBN 978-3-319-54207-2/pbk; 978-3-319-54208-9/ebook). Lecture Notes in Mathematics 2183, 141-176 (2017). Reviewer: Christopher Policastro (Berkeley) MSC: 35B40 35D40 35F21 49R99 PDF BibTeX XML Cite \textit{N. Q. Le} et al., Lect. Notes Math. 2183, 141--176 (2017; Zbl 1382.35040) Full Text: DOI
Le, Nam Q.; Mitake, Hiroyoshi; Tran, Hung V. Ergodic problems for Hamilton-Jacobi equations. (English) Zbl 1400.35070 Mitake, Hiroyoshi (ed.) et al., Dynamical and geometric aspects of Hamilton-Jacobi and linearized Monge-Ampére equations. VIASM 2016. Based on lectures at the Rutgers University, NJ, USA, 2013. Cham: Springer (ISBN 978-3-319-54207-2/pbk; 978-3-319-54208-9/ebook). Lecture Notes in Mathematics 2183, 129-139 (2017). Reviewer: Philippe Laurençot (Toulouse) MSC: 35F21 35D40 35K15 35B40 35K65 PDF BibTeX XML Cite \textit{N. Q. Le} et al., Lect. Notes Math. 2183, 129--139 (2017; Zbl 1400.35070) Full Text: DOI
Mitake, Hiroyoshi; Tran, Hung V. Part II: Dynamical properties of Hamilton-Jacobi equations via the nonlinear adjoint method: large time behavior and discounted approximation. (English) Zbl 1373.35004 Mitake, Hiroyoshi (ed.) et al., Dynamical and geometric aspects of Hamilton-Jacobi and linearized Monge-Ampére equations. VIASM 2016. Based on lectures at the Rutgers University, NJ, USA, 2013. Cham: Springer (ISBN 978-3-319-54207-2/pbk; 978-3-319-54208-9/ebook). Lecture Notes in Mathematics 2183, 125-128 (2017). MSC: 35-02 35F21 35B40 PDF BibTeX XML Cite \textit{H. Mitake} and \textit{H. V. Tran}, Lect. Notes Math. 2183, 125--128 (2017; Zbl 1373.35004)
Le, Nam Q.; Mitake, Hiroyoshi; Tran, Hung V. The Monge-Ampère equation. (English) Zbl 1392.35004 Mitake, Hiroyoshi (ed.) et al., Dynamical and geometric aspects of Hamilton-Jacobi and linearized Monge-Ampére equations. VIASM 2016. Based on lectures at the Rutgers University, NJ, USA, 2013. Cham: Springer (ISBN 978-3-319-54207-2/pbk; 978-3-319-54208-9/ebook). Lecture Notes in Mathematics 2183, 73-123 (2017). Reviewer: Vincenzo Vespri (Firenze) MSC: 35-02 35J96 35B50 35B51 PDF BibTeX XML Cite \textit{N. Q. Le} et al., Lect. Notes Math. 2183, 73--123 (2017; Zbl 1392.35004) Full Text: DOI
Le, Nam Q.; Mitake, Hiroyoshi; Tran, Hung V. The linearized Monge-Ampère equation. (English) Zbl 1392.35003 Mitake, Hiroyoshi (ed.) et al., Dynamical and geometric aspects of Hamilton-Jacobi and linearized Monge-Ampére equations. VIASM 2016. Based on lectures at the Rutgers University, NJ, USA, 2013. Cham: Springer (ISBN 978-3-319-54207-2/pbk; 978-3-319-54208-9/ebook). Lecture Notes in Mathematics 2183, 35-72 (2017). Reviewer: Vincenzo Vespri (Firenze) MSC: 35-02 35J96 PDF BibTeX XML Cite \textit{N. Q. Le} et al., Lect. Notes Math. 2183, 35--72 (2017; Zbl 1392.35003) Full Text: DOI
Le, Nam Q.; Mitake, Hiroyoshi; Tran, Hung V. The affine Bernstein and boundary value problems. (English) Zbl 1378.35002 Mitake, Hiroyoshi (ed.) et al., Dynamical and geometric aspects of Hamilton-Jacobi and linearized Monge-Ampére equations. VIASM 2016. Based on lectures at the Rutgers University, NJ, USA, 2013. Cham: Springer (ISBN 978-3-319-54207-2/pbk; 978-3-319-54208-9/ebook). Lecture Notes in Mathematics 2183, 7-33 (2017). Reviewer: Giuseppe Di Fazio (Catania) MSC: 35-02 35J62 35B65 35J96 35B50 PDF BibTeX XML Cite \textit{N. Q. Le} et al., Lect. Notes Math. 2183, 7--33 (2017; Zbl 1378.35002) Full Text: DOI
Ishii, Hitoshi; Mitake, Hiroyoshi; Tran, Hung V. The vanishing discount problem and viscosity Mather measures. II: Boundary value problems. (English. French summary) Zbl 1375.35183 J. Math. Pures Appl. (9) 108, No. 3, 261-305 (2017). MSC: 35J60 35J70 35A15 PDF BibTeX XML Cite \textit{H. Ishii} et al., J. Math. Pures Appl. (9) 108, No. 3, 261--305 (2017; Zbl 1375.35183) Full Text: DOI
Ishii, Hitoshi; Mitake, Hiroyoshi; Tran, Hung V. The vanishing discount problem and viscosity Mather measures. 1: The problem on a torus. (English. French summary) Zbl 1375.35182 J. Math. Pures Appl. (9) 108, No. 2, 125-149 (2017). MSC: 35J60 35J70 35A15 PDF BibTeX XML Cite \textit{H. Ishii} et al., J. Math. Pures Appl. (9) 108, No. 2, 125--149 (2017; Zbl 1375.35182) Full Text: DOI
Mitake, Hiroyoshi (ed.); Tran, Hung V. (ed.) Dynamical and geometric aspects of Hamilton-Jacobi and linearized Monge-Ampére equations. VIASM 2016. Based on lectures at the Rutgers University, NJ, USA, 2013. (English) Zbl 1373.35006 Lecture Notes in Mathematics 2183. Cham: Springer (ISBN 978-3-319-54207-2/pbk; 978-3-319-54208-9/ebook). vii, 228 p. (2017). MSC: 35-06 35B10 35B40 35B50 35B51 35B65 35J40 PDF BibTeX XML Cite \textit{H. Mitake} (ed.) and \textit{H. V. Tran} (ed.), Dynamical and geometric aspects of Hamilton-Jacobi and linearized Monge-Ampére equations. VIASM 2016. Based on lectures at the Rutgers University, NJ, USA, 2013. Cham: Springer (2017; Zbl 1373.35006) Full Text: DOI
Mitake, Hiroyoshi; Tran, Hung V. Selection problems for a discount degenerate viscous Hamilton-Jacobi equation. (English) Zbl 1357.35090 Adv. Math. 306, 684-703 (2017). MSC: 35F21 35B40 37J50 49L25 PDF BibTeX XML Cite \textit{H. Mitake} and \textit{H. V. Tran}, Adv. Math. 306, 684--703 (2017; Zbl 1357.35090) Full Text: DOI
Mitake, H.; Tran, H. V. Weakly coupled systems of the infinity Laplace equations. (English) Zbl 1359.35054 Trans. Am. Math. Soc. 369, No. 3, 1773-1795 (2017). Reviewer: Marius Ghergu (Dublin) MSC: 35J47 35D40 35J70 49L20 PDF BibTeX XML Cite \textit{H. Mitake} and \textit{H. V. Tran}, Trans. Am. Math. Soc. 369, No. 3, 1773--1795 (2017; Zbl 1359.35054) Full Text: DOI
Giga, Yoshikazu; Mitake, Hiroyoshi; Tran, Hung V. On asymptotic speed of solutions to level-set mean curvature flow equations with driving and source terms. (English) Zbl 1355.35123 SIAM J. Math. Anal. 48, No. 5, 3515-3546 (2016). MSC: 35K93 35B40 35K20 35Q92 PDF BibTeX XML Cite \textit{Y. Giga} et al., SIAM J. Math. Anal. 48, No. 5, 3515--3546 (2016; Zbl 1355.35123) Full Text: DOI arXiv
Mitake, H.; Siconolfi, A.; Tran, H. V.; Yamada, N. A Lagrangian approach to weakly coupled Hamilton-Jacobi systems. (English) Zbl 1343.35065 SIAM J. Math. Anal. 48, No. 2, 821-846 (2016). MSC: 35F21 35F50 49L25 37K55 PDF BibTeX XML Cite \textit{H. Mitake} et al., SIAM J. Math. Anal. 48, No. 2, 821--846 (2016; Zbl 1343.35065) Full Text: DOI arXiv
Mitake, Hiroyoshi; Tran, Hung V. Large-time behavior for obstacle problems for degenerate viscous Hamilton-Jacobi equations. (English) Zbl 1327.35065 Calc. Var. Partial Differ. Equ. 54, No. 2, 2039-2058 (2015). MSC: 35F21 35B40 35F55 49L25 PDF BibTeX XML Cite \textit{H. Mitake} and \textit{H. V. Tran}, Calc. Var. Partial Differ. Equ. 54, No. 2, 2039--2058 (2015; Zbl 1327.35065) Full Text: DOI arXiv
Cagnetti, Filippo; Gomes, Diogo; Mitake, Hiroyoshi; Tran, Hung V. A new method for large time behavior of degenerate viscous Hamilton-Jacobi equations with convex Hamiltonians. (English) Zbl 1312.35020 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 32, No. 1, 183-200 (2015). MSC: 35B40 35F55 49L25 35F21 35K65 35D40 PDF BibTeX XML Cite \textit{F. Cagnetti} et al., Ann. Inst. Henri Poincaré, Anal. Non Linéaire 32, No. 1, 183--200 (2015; Zbl 1312.35020) Full Text: DOI arXiv
Mitake, Hiroyoshi; Tran, Hung V. Homogenization of weakly coupled systems of Hamilton-Jacobi equations with fast switching rates. (English) Zbl 1297.35022 Arch. Ration. Mech. Anal. 211, No. 3, 733-769 (2014). Reviewer: Adrian Muntean (Eindhoven) MSC: 35B27 35F21 35B40 PDF BibTeX XML Cite \textit{H. Mitake} and \textit{H. V. Tran}, Arch. Ration. Mech. Anal. 211, No. 3, 733--769 (2014; Zbl 1297.35022) Full Text: DOI arXiv
Mitake, H.; Tran, H. V. A dynamical approach to the large-time behavior of solutions to weakly coupled systems of Hamilton-Jacobi equations. (English) Zbl 1278.35020 J. Math. Pures Appl. (9) 101, No. 1, 76-93 (2014). MSC: 35B40 35F55 49L25 35F61 35F21 35Q93 35D40 PDF BibTeX XML Cite \textit{H. Mitake} and \textit{H. V. Tran}, J. Math. Pures Appl. (9) 101, No. 1, 76--93 (2014; Zbl 1278.35020) Full Text: DOI
Mitake, Hiroyoshi; Tran, Hung V. Remarks on the large time behavior of viscosity solutions of quasi-monotone weakly coupled systems of Hamilton-Jacobi equations. (English) Zbl 1241.35020 Asymptotic Anal. 77, No. 1-2, 43-70 (2012). MSC: 35B40 35D40 35F21 PDF BibTeX XML Cite \textit{H. Mitake} and \textit{H. V. Tran}, Asymptotic Anal. 77, No. 1--2, 43--70 (2012; Zbl 1241.35020) Full Text: Link arXiv