For the most part, our work on the analysis of partial differential equations (PDEs) is motivated by the need to obtain results that are then used in the numerical analysis of discretization algorithms for the PDEs. Often, the PDE results are incorporated into the numerical analysis paper, so that in addition to the papers listed below, many other papers found on other web pages of this site also contain PDE analyses.
M. Gunzburger and Q. Du; Analysis of a Ladyzhenskaya model for incompressible viscous flow, J. Math. Anal. Appl. 155 1991, 21-45.
A. Fursikov, M. Gunzburger, and L. Hou; Boundary value problems and optimal boundary control for the Navier-Stokes system: The two-dimensional case, SIAM J. Cont. Optim. 36 1998, 852-894.
M. Gunzburger, H.-C. Lee, and G. Seregin; Global existence of weak solutions for incompressible viscous flow around a moving rigid body in three dimensions, J. Math. Fluid Mech. 2 2000, 219-266.
M. Gunzburger and H.-C. Lee; Analysis of some boundary value problems for Stokes flows, Kyungpook Math. J. 35 1996, 501-512.
A. Fursikov, M. Gunzburger, and L. Hou; Trace theorems for three-dimensional, time-dependent solenoidal vector fields and their applications, Trans. Amer. Math. Soc. 354 2001, 1079-1116.
A. Fursikov, M. Gunzburger, and L. Hou; Inhomogeneous boundary value problems for the three-dimensional evolutionary Navier-Stokes equations, J. Math. Fluid Mech. 4 2002, 45-75.
Q. Du, M. Gunzburger, L. Hou, and J. Lee; Analysis of a linear fluid-structure interaction problem, Disc. Cont. Dyn. Sys. 9 2003, 633-650.
M. Gunzburger, and O. Ladyzhenskaya, and J. Peterson; On the global unique solvability of initial-boundary value problems for the coupled modified Navier-Stokes and Maxwell equations, J. Math. Fluid Mech. 6 2004, 462-482.
A. Fursikov, M. Gunzburger, and L. Hou; Optimal boundary control for the evolutionary Navier-Stokes system: the three-dimensional case, SIAM J. Cont. Optim. 43 2005, 2191-2232.
M. Gunzburger, L. Hou, and W. Zhu; Modeling and analysis of the forced Fisher equation, Nonlin. Anal.: Theo. Meth. Appl. 62 2005, 19-40.
M. Gunzburger and C. Trenchea; Optimal control of the time-periodic MHD equations, Nonlin. Anal.: Theo. Meth. Appl. 63 2005, e1687-e1699.
M. Gunzburger, Y. Saka, and X. Wang; Well-posedness of the infinite Prandtl number model for convection with temperature-dependent viscosity, Anal. Appl. 7 2009, 297-308.
A. Fursikov, M. Gunzburger, and J. Peterson; The Ginzburg-Landau equations for superconductivity with random fluctuations, Sobolev Spaces in Mathematics III: Applications in Mathematical Physics, Springer, Berlin, 2009, 25-133.
Last updated: 12/29/09 by Max Gunzburger