TY - JOUR
T1 - Asymptotics of the principal eigenvalue for a linear time-periodic parabolic operator i
T2 - Large advection
AU - Liu, Shuang
AU - Lou, Yuan
AU - Peng, Rui
AU - Zhou, Maolin
N1 - Publisher Copyright:
© 2021 Society for Industrial and Applied Mathematics
PY - 2021
Y1 - 2021
N2 - We investigate the effect of large advection on the principal eigenvalues of linear time-periodic parabolic operators with zero Neumann boundary conditions. Various asymptotic behaviors of the principal eigenvalues, when the advection coefficient approaches infinity, are established, where spatial or temporal degeneracy could occur in the advection term. Our findings substantially improve the results in [R. Peng and X.-Q. Zhao, Calc. Var. Partial Differential Equations, 54 (2015), pp. 1611-1642] for parabolic operators and also extend the existing results in [X. F. Chen and Y. Lou, Indiana Univ. Math. J., 57 (2008), pp. 627-658; R. Peng and M. Zhou, Indiana Univ. Math J., 67 (2018), pp. 2523-2568] for elliptic operators.
AB - We investigate the effect of large advection on the principal eigenvalues of linear time-periodic parabolic operators with zero Neumann boundary conditions. Various asymptotic behaviors of the principal eigenvalues, when the advection coefficient approaches infinity, are established, where spatial or temporal degeneracy could occur in the advection term. Our findings substantially improve the results in [R. Peng and X.-Q. Zhao, Calc. Var. Partial Differential Equations, 54 (2015), pp. 1611-1642] for parabolic operators and also extend the existing results in [X. F. Chen and Y. Lou, Indiana Univ. Math. J., 57 (2008), pp. 627-658; R. Peng and M. Zhou, Indiana Univ. Math J., 67 (2018), pp. 2523-2568] for elliptic operators.
KW - Advection
KW - Asymptotics
KW - Principal eigenvalue
KW - Time-periodic parabolic operator
UR - http://www.scopus.com/inward/record.url?scp=85118215876&partnerID=8YFLogxK
U2 - 10.1137/20M1379563
DO - 10.1137/20M1379563
M3 - Article
AN - SCOPUS:85118215876
SN - 0036-1410
VL - 53
SP - 5243
EP - 5277
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
IS - 5
ER -