메뉴 건너뛰기




Volumn 36, Issue 4, 2011, Pages 693-728

Gevrey Hypoellipticity for a Class of Kinetic Equations

Author keywords

Gevrey regularity; Kinetic equation; Microlocal analysis

Indexed keywords


EID: 78951470972     PISSN: 03605302     EISSN: 15324133     Source Type: Journal    
DOI: 10.1080/03605302.2010.507689     Document Type: Article
Times cited : (26)

References (22)
  • 3
    • 18844411595 scopus 로고    scopus 로고
    • Littlewood Paley decomposition and regularity issues in Boltzmann equation homogeneous equations. I. Non cutoff and Maxwell cases
    • Alexandre, R., Safadi, M. (2005). Littlewood Paley decomposition and regularity issues in Boltzmann equation homogeneous equations. I. Non cutoff and Maxwell cases. Math. Models Methods Appl. Sci. 15:907-920.
    • (2005) Math. Models Methods Appl. Sci. , vol.15 , pp. 907-920
    • Alexandre, R.1    Safadi, M.2
  • 4
    • 84975095863 scopus 로고    scopus 로고
    • Hypoelliptic regularity in kinetic equations
    • Bouchut, F. (2002). Hypoelliptic regularity in kinetic equations. J. Math. Pure Appl. 81:1135-1159.
    • (2002) J. Math. Pure Appl. , vol.81 , pp. 1135-1159
    • Bouchut, F.1
  • 5
    • 55249097148 scopus 로고    scopus 로고
    • Gevrey hypoellipticity for linear and nonlinear Fokker-Planck equations
    • Chen, H., Li, W.-X., Xu, C.-J. (2009). Gevrey hypoellipticity for linear and nonlinear Fokker-Planck equations. J. Diff. Eqs. 246:320-339.
    • (2009) J. Diff. Eqs. , vol.246 , pp. 320-339
    • Chen, H.1    Li, W.-X.2    Xu, C.-J.3
  • 6
    • 1642620131 scopus 로고    scopus 로고
    • General theory of PDE and Gevrey class
    • In: Qi, M.-Y., Rodino, L., eds., Pitman Research Notes in Mathematics, Harlow, England: Longman
    • Chen, H., Rodino, L. (1996). General theory of PDE and Gevrey class. In: Qi, M.-Y., Rodino, L., eds., General Theory of Partial Differential Equations and Microlocal Analysis. Pitman Research Notes in Mathematics, Vol. 349. Harlow, England: Longman, pp. 6-81.
    • (1996) General Theory of Partial Differential Equations and Microlocal Analysis , vol.349 , pp. 6-81
    • Chen, H.1    Rodino, L.2
  • 7
    • 0010909671 scopus 로고
    • Sur la régularité Gevrey des opérateurs de Hörmander
    • Derridj, M., Zuily, C. (1973). Sur la régularité Gevrey des opérateurs de Hörmander [Gevrey regularity of Hörmander's operators]. J. Math. Pure Appl. 52:309-336.
    • (1973) J. Math. Pure Appl. , vol.52 , pp. 309-336
    • Derridj, M.1    Zuily, C.2
  • 8
    • 67349233256 scopus 로고    scopus 로고
    • Propagation of Gevrey regularity for solutions of Boltzmann equation for Maxwellian molecules
    • Desvillettes, L., Furioli, G., Terraneo, E. (2009). Propagation of Gevrey regularity for solutions of Boltzmann equation for Maxwellian molecules. Trans. Amer. Math. Soc. 361:1731-1747.
    • (2009) Trans. Amer. Math. Soc. , vol.361 , pp. 1731-1747
    • Desvillettes, L.1    Furioli, G.2    Terraneo, E.3
  • 9
    • 1642284756 scopus 로고    scopus 로고
    • Smoothness of the solution of the spatially homogeneous Boltzmann equation without cutoff
    • Desvillettes, L., Wennberg, B. (2004). Smoothness of the solution of the spatially homogeneous Boltzmann equation without cutoff. Comm. Part. Diff. Eqs. 29:133-155.
    • (2004) Comm. Part. Diff. Eqs. , vol.29 , pp. 133-155
    • Desvillettes, L.1    Wennberg, B.2
  • 10
    • 55249125516 scopus 로고
    • Régularité Gevrey d'une classe d'opérateurs hypoelliptiques
    • Durand, M. (1978). Régularité Gevrey d'une classe d'opérateurs hypoelliptiques [Gevrey regularity of a class of hypo-elliptic operators]. J. Math. Pure Appl. 57:323-360.
    • (1978) J. Math. Pure Appl. , vol.57 , pp. 323-360
    • Durand, M.1
  • 11
    • 0000270362 scopus 로고
    • On the regularity of the solutions of non-linear elliptic and parabolic systems of partial differential equations
    • Friedman, A. (1958). On the regularity of the solutions of non-linear elliptic and parabolic systems of partial differential equations. J. Math. Mech. 7:43-59.
    • (1958) J. Math. Mech. , vol.7 , pp. 43-59
    • Friedman, A.1
  • 13
    • 1142264370 scopus 로고    scopus 로고
    • Isotropic hypoellipticity and trend to equilibrium for the Fokker-Planck equation with a high-degree potential
    • Hérau, F., Nier, F. (2004). Isotropic hypoellipticity and trend to equilibrium for the Fokker-Planck equation with a high-degree potential. Arch. Ration. Mech. Anal. 171:151-218.
    • (2004) Arch. Ration. Mech. Anal. , vol.171 , pp. 151-218
    • Hérau, F.1    Nier, F.2
  • 16
    • 35348971478 scopus 로고    scopus 로고
    • Hypoellipticity for a class of kinetic equations
    • Morimoto, Y., Xu, C.-J. (2007). Hypoellipticity for a class of kinetic equations. J. Math. Kyoto Univ. 47:129-152.
    • (2007) J. Math. Kyoto Univ. , vol.47 , pp. 129-152
    • Morimoto, Y.1    Xu, C.-J.2
  • 17
    • 67349092273 scopus 로고    scopus 로고
    • Ultra-analytic effect of Cauchy problem for a class of kinetic equations
    • Morimoto, Y., Xu, C.-J. (2009). Ultra-analytic effect of Cauchy problem for a class of kinetic equations. J. Diff. Eqs. 247:596-617.
    • (2009) J. Diff. Eqs. , vol.247 , pp. 596-617
    • Morimoto, Y.1    Xu, C.-J.2
  • 20
    • 0003244114 scopus 로고
    • Local solutions in Gevrey classes to the nonlinear Boltzmann equation without cutoff
    • Ukai, S. (1984). Local solutions in Gevrey classes to the nonlinear Boltzmann equation without cutoff. Japan J. Appl. Math. 1(1):141-156.
    • (1984) Japan J. Appl. Math. , vol.1 , Issue.1 , pp. 141-156
    • Ukai, S.1
  • 21
    • 0032338727 scopus 로고    scopus 로고
    • On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations
    • Villani, C. (1998). On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations. Arc. Rational Mech. Anal. 143:273-307. [22] Xu, C.-J. (1996). Nonlinear microlocal analysis. In: Qi, M.-Y., Rodino, L., eds., General Theory of Partial Differential Equations and Microlocal Analysis. Pitman Research Notes in Mathematics, Vol. 349. Harlow, England: Longman, pp. 155-182.
    • (1998) Arc. Rational Mech. Anal. , vol.143 , pp. 273-307
    • Villani, C.1
  • 22
    • 55249093942 scopus 로고    scopus 로고
    • Nonlinear microlocal analysis
    • In: Qi, M.-Y., Rodino, L., eds., Pitman Research Notes in Mathematics, Harlow, England: Longman
    • Xu, C.-J. (1996). Nonlinear microlocal analysis. In: Qi, M.-Y., Rodino, L., eds., General Theory of Partial Differential Equations and Microlocal Analysis. Pitman Research Notes in Mathematics, Vol. 349. Harlow, England: Longman, pp. 155-182
    • (1996) General Theory of Partial Differential Equations and Microlocal Analysis , vol.349 , pp. 155-182
    • Xu, C.-J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.