Research interest: curvature flow,reaction-diffusion equation
I.The curvature flows with constraint, or nonlocal flows
(1)Tsai Dong-Ho*, Wang Xiaoliu*, The evolution of nonlocal curvature flow arising in a Hele-Shaw problem. SIAM J. Math. Anal., in press, 2018.
(2)Sesum Natasa*, Tsai Dong-Ho, Wang Xiao-Liu, Evolution of Locally Convex Closed Curves in Nonlocal Curvature Flows. Submitted, 2017.
(3)Wang Xiaoliu*, Li Huiling, Chao Xiaoli, Length-preserving evolution of immersed closed curves and the isoperimetric inequality, Pacific J. Math.290(2017),no. 2, 467–479.
(4)Wang Xiaoliu *, Wo Weifeng, Yang Ming, Evolution of non-simple closed curves in the area-preserving curvature flow, Proc. Roy. Soc. Edinburgh Sect. A, DOI 10.1017/S0308210517000269, 2018.
(5)Tsai Dongho*, Wang Xiaoliu, On length-preserving and area-preserving nonlocal flow of convex closed plane curves, Calc. Var. Partial Differential Equations, 54 (2015) 3603–3622.
(6)Wang Xiaoliu, Wo Weifeng*, Length-preserving evolution of non-simple symmetric plane curves, Math. Methods Appl. Sci., 37 (2014) 808-816.
(7)Wang Xiaoliu *, Kong Linghua, Area-preserving evolution of non-simple symmetric plane curves, J. Evol. Equ., 14 (2014) 387-401.
(8)Chao Xiaoli, Ling Xiaoran, Wang Xiaoliu *, On a planar area-preserving curvature flow, Proc. Amer. Math. Soc., 141 (2013) 1783-1789.
II.The shrinking curvature flows
(1)Wo Weifeng, Wang Xiaoliu, Qu Changzheng*, The centro-affine invariant geometric heat flow, Math. Z., DOI 10.1007/s00209-017-1890-3,2017.
(2)Chen Wenyan, Wang Xiaoliu *, Yang Ming, Evolution of highly symmetric curves under the shrinking curvature flow, Math. Meth. Appl. Sci. 40(2017) 3775-3783.
(3)Wo Weifeng*, Yang Shuxin, Wang Xiaoliu, Group invariant solutions to a centro-affine invariant flow, Arch. Math. (Basel), online publication, 2017, DOI:10.1007/s00013-016-1010-3.
(4)Chou Kaiseng, Wang Xiaoliu *, A note on Abresch-Langer conjecture, Proc. Roy. Soc. Edinburgh Sect. A, 144 (2014) 299-304.
(5)Chou Kaiseng, Wang Xiaoliu *, The curve shortening problem under robin boundary condition, NoDEA Nonlinear Differential Equations Appl., 19 (2012) 177-194.
(6)Wang Xiaoliu, Wo Weifeng*, On the asymptotic stability of stationary lines in the curve shortening problem, Pure Appl. Math. Q., 9 (2013) 493-506.
(7)Wang Xiaoliu *, Wo Weifeng, On the stability of stationary line and grim reaper in planar curvature flow, Bull. Aust. Math. Soc., 83 (2011) 177-188.
(8)Wang Xiaoliu *, The stability of m-fold circles in the curve shortening problem, Manuscripta Math.,134 (2011) 493-511.
III Other curvature flows
(1) Lin Yuchu, Tsai Dongho*, Wang Xiaoliu, On some simple examples of non-parabolic curve flows in the plane, J. Evol. Equ., 15 (2015) 817–845.
IV Nonlinear Parabolic PDEs
(1)Wang Hengling, Tao Weirun, Wang Xiaoliu*, Finite-time blow-up and global convergence of solutions to a nonlocal parabolic equation with conserved spatial integral, Nonlinear Analysis Real World Applications, 40 (2018) 55-63.
(2)Li Huiling, Wang Hengling, Wang Xiaoliu*, A quasilinear parabolic problem with a source term and a nonlocal absorption, Communications on Pure and Applied Analysis, in press, 2018.
(3)Wang Xiaoliu*, Tian Fangzheng, Li Gen, Nonlocal parabolic equation with conserved spatial integral, Arch. Math. (Basel) , 105 (2015) 93–100.
(4)Kong Linghua,Wang Xiaoliu, Xueda Zhao*, Asymptotic analysis to a parabolic system with weighted localized sources and inner absorptions, Arch. Math. (Basel), 99 (2012) 375-386.
(5)Liu Zhe,Wang Xiaoliu*, On a parabolic equation in MEMS with fringing field, Arch. Math. (Basel), 98 (2012) 373-381.
(6)Wang Xiaoliu*, Wo Weifeng, Long time behavior of solutions for a scalar nonlocal reaction-diffusion equation, Arch. Math. (Basel), 96 (2011) 483-490.
(7)Wang Mingxin*,Wang Xiaoliu, A reaction-diffusion system with nonlinear absorption terms and boundary flux, Acta Math. Appl. Sin. Engl. Ser., 24 (2008) 409-422.
V Geometry on surfaces
(1) Wang, Xiaoliu; Chao, Xiaoli*, Constant angle surfaces constructed on curves. J. Southeast Univ. (English Ed.) 29 (2013) 470–472.
