Time-periodic solutions of nonlinear partial differential equations
Jon Wilkening, Breakdown of self-similarity at the crests of large amplitude standing water waves,
Phys. Rev. Lett, 107, 184501, 2011.
water1.pdf
M. O. Williams, E. Shlizerman, J. Wilkening and J. N. Kutz, The low dimensionality of
time-periodic standing waves in water of finite and infinite depth, SIAM J. Appl. Dyn. Syst., 2012
(revised 4/20/2012).
water_pod.pdf
M. O. Williams, J. Wilkening, E. Shlizerman and J. N. Kutz, Continuation of periodic solutions
in the waveguide array mode-locked laser, Physica D, 240/22 (2011), pp. 1791-1804.
laser.pdf
David M. Ambrose and Jon Wilkening, Dependence of time-periodic vortex sheets with surface tension
on mean vortex sheet strength, 2010 (submitted to Phys. Fluids).
vtxs2.pdf
David M. Ambrose and Jon Wilkening, Computation of symmetric, time-periodic
solutions of the vortex sheet with surface tension, Proc. Natl. Acad. Sci.,
107/8 (2010), pp. 3361-3366.
vtxs1.pdf
David M. Ambrose and Jon Wilkening, Computing time-periodic solutions of
nonlinear systems of partial differential equations,
Hyperbolic Problems: Theory, Numerics, and Applications, Proceedings of the
13th International Conference on Hyperbolic Problems, held in
Beijing, China, June 15-19, 2010.
vtxs3.pdf
David M. Ambrose and Jon Wilkening, Computation of time-periodic
solutions of the
Benjamin-Ono equation, J. Nonlinear Sci., 20/3 (2010), pp. 277-308.
benj1.pdf
David M. Ambrose and Jon Wilkening, Global paths of time-periodic solutions
of the Benjamin-Ono equation connecting pairs of traveling waves,
Comm. App. Math. and Comp. Sci., 4/1 (2009), pp. 177-215.
benj2.pdf
Jon Wilkening, An infinite branching hierarchy of time-periodic
solutions of the Benjamin-Ono equation, arXiv:0811.4209.
benj3.pdf
Shape optimization and analysis of lubrication theory
Jon Wilkening, Practical error estimates for Reynolds' lubrication
approximation and its higher order corrections,
SIAM J. Math. Anal., 41/2 (2009), pp. 588-630.
rle.pdf
Jon Wilkening, Inf-sup estimates for the Stokes problem in a
periodic channel, arXiv:0706.4082.
infsup.pdf
Jon Wilkening, A. E. Hosoi, Shape optimization of a sheet
swimming over a thin liquid layer,
J. Fluid Mech., 601 (2008), pp. 25-61.
snail.pdf
Dirichlet to Neumann operators and semi-group theory in the analysis
of grain boundary diffusion in materials science
L. C. Lee, S. J. S. Morris and J. Wilkening, Stress concentrations, diffusionally-accommodated
grain boundary sliding and the viscoelasticity of polycrystals, Proc. Royal Soc. A, 467 (2011), pp. 1624-1644.
gb-sliding.pdf
J. Wilkening, L. Borucki, J. A. Sethian, Analysis of stress-driven
grain boundary diffusion, part I, SIAM J. Appl. Math. 64/6 (2004),
pp. 1839-1863.
gb-diff1.pdf
J. Wilkening, L. Borucki, J. A. Sethian, Analysis of stress-driven
grain boundary diffusion, part II: degeneracy, SIAM J. Appl. Math.
64/6 (2004), pp. 1864-1886. gb-diff2.pdf
J. A. Sethian, J. Wilkening, A numerical model of stress driven
grain boundary diffusion, J. Comput. Phys., 193/1 (2003), pp. 275-305.
gb-num.pdf
J. Wilkening, Mathematical Analysis and Numerical Simulation of
Electromigration, PhD thesis, University of California, Berkeley, May
2002.
Optimal transportation and geodesic flows in the Wasserstein metric
Michael Westdickenberg and Jon Wilkening, Variational particle scheme for
the porous medium equation and for the system of isentropic Euler equations,
ESAIM-Math. Model. Num., 44 (2010), pp. 133-166.
VarScheme.pdf
Matrix factorizations and canonical forms
Jon Wilkening and Jia Yu, A local construction of the Smith normal
form of a matrix polynomial,
J. Symbolic Comput., 46 (2011), pp. 1-22.
smith.pdf
J. Wilkening, An algorithm for computing Jordan chains and inverting
analytic matrix functions, Linear Algebra Appl., 427/1 (2007), pp. 6-25.
Achain.pdf