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. , 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, 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.
