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Papers
that Evolved Directly from the Industrial Problems Seminar

1

G.
Bao, An inverse diffraction problem in periodic structures,
proceedings of third international conference on mathematical
and numerical aspects of wave propagation, ed. by G. Cohen,
SIAM, Philadelphia, 694--704, 1995.

2

G.
Bao, A uniqueness theorem for an inverse problem in periodic
diffractive optics, Inverse Problems 10 (1994), 335--340.

3

G.
Bao, Direct and inverse diffraction by periodic structures,
in the proceedings of international conference on nonlinear
PDE and applications, submitted.

4

G. Bao, Finite element approximation of time harmonic waves
in periodic structures, SIAM J. Numerical Analysis 32, No. 4
(1995), 1155--1169.

5

G. Bao, Inverse diffraction by a periodic perfect conductor
with several measurements, in the proceedings of 2nd international
conference on inverse problems in engineering, to appear.

G. Bao, Numerical analysis of diffraction by periodic structures: TM polarization, numerische mathematik 75 (1996), 1--16.

7

G. Bao, Regularity of an inverse diffraction problem, inverse problems, submitted.

8

G. Bao, Variational approximation of Maxwell's equations in biperiodic structures, SIAM J. Appl. Math. 57, No. 2 (1997), 364--381.

9

G. Bao, Y. Cao and H. Yang, Least-squares finite element computation of diffraction problems, SIAM J. Sci. Comput., submitted.

10

G. Bao and Y. Chen, A nonlinear grating problem in diffractive optics, SIAM J. Math. Anal. 2 (1997), 322--337.

11

G. Bao and D. Dobson, Diffractive optics in nonlinear media with period structures, IMA Preprint Series # 1124, March 1993, University of Minnesota, Minneapolis.

12

G. Bao and D. Dobson, Diffractive optics in nonlinear media with period structures, Euro. J. Appl. Math. 6 (1995), 573--590.

13

G. Bao and D. Dobson, Modeling and optimal design of diffractive optical structures, submitted to Surveys on Math. for Industry.

14

G. Bao and D. Dobson, Nonlinear optics in periodic diffraction structures, Second international Conference on mathematical and numerical aspects of wave propagation, ed. by R. Kleinman, T. Angell, D. Colton, F. Santosa, and I. Stak gold, SIAM, Philadephia, 30--38, 1993.

15

G. Bao and D. Dobson, Second harmonic generation in nonlinear optical films, J. Math. Physics 35 (1994), 1622--1633.

16

G. Bao, D. Dobson, and J.A. Cox, Mathematical issues in the electromagnetic theory of gratings, in diffractive optics: design, fabrication and applications, technical digest, Optical Society of American 11 (1994), 8--11.

17

G. Bao, D. Dobson, and J.A. Cox, Mathematical studies in rigorous grating theory, J. Opt. Soc, Amer. A 12 (1995), 573--590.

18

G. Bao and H. Yang, Least-squares finite elements computation of diffraction problems, SIAM J. Sci. Comput., submitted.

19

G. Bao and Y. Chen, A nonlinear grating problem in diffractive optics, SIAM J. Math. Anal. 8, No. 2 (1997), 322-337.

20

G. Bao and Z. Zhou, Inverse diffraction by a doubly periodic structure, C.R. Acad. Sci., Paris, Serie I, t 324 (1997), 627-632.

21

G. Bao and Z. Zhou, An inverse problem for scattering by a doubly periodic structure, AMS Trans., to appear.

22

G. Bao and A. Friedman, Inverse problems for scattering by periodic structure, Archive Rat. Mech. Anal. 132 (1995), 49--72.

23

H. Bellout and A. Friedman, Scattering by stripe grating, J. Math. Anal. Appl. 147 (1990), 228--248.

24

O.P. Bruno and F. Reitich, A new approach to the solution of problems of scattering by bounded obstacles, in SPIE 2192, Mathematics and control in smart structures (1994), H.T. Banks, ed., 20--28.

25

O.P. Bruno and F. Reitich, Accurate calculation of diffractive grating efficiencies, SPIE 1919, Mathematics in Smart Structures (1993), 236--247.

26

O.P. Bruno and F. Reitich, Approximation of analytic functions: a method of enhanced convergence, Math. Comp. 63 (1994), 195--213.

27

O.P. Bruno and F. Reitich, Boundary-variation solutions for bounded-obstacle scattering in three dimensions, submitted to J. Comp. Phys. (1997).

28

O.P. Bruno and F. Reitich, Calculation of electromagnetic scattering via boundary variations and analytic continuation, ACES J. 11 (1996), 17--31.

29

O.P. Bruno and F. Reitich, Maxwell equations in a nonlinear Kerr medium, Proc. R. Soc. Lond. A 447 (1994), 65--76.

30

O.P. Bruno and F. Reitich, Numerical solution of diffraction problems: A method of variation of boundaries, J. Optical Soc. Amer. A. 10 (1993), 1168--1175.

31

O.P. Bruno and F. Reitich, Numerical solution of diffraction problems: a method of variation of boundaries, J. Opt. Soc. Am. A 10 (1993), 1168--1175.

32

O.P. Bruno and F. Reitich, Numerical solution of diffraction problems: a method of variation of boundaries II, Dielectric gratings, Pade approximants and singularities, J. Optical Soc. Amer. A 10 (1993), 2307--2316.

33

O.P. Bruno and F. Reitich, Numerical solution of diffraction problems: a method of variation of boundaries III. Doubly-periodic gratings, J. Optical Soc. Amer. A 10 (1993), 2551--2562.

34

O.P. Bruno and F. Reitich, Solution of a boundary value problem for Helmhotz equation of the boundary into the complex domain, Proc. Roy. Soc. Edinburg, 122A (1992), 317--340.

35

O.P. Bruno, A. Friedman, and F. Reitich, Asymptotic behavior for a coalescence problem, Trans. Amer. Math. Soc. 338 (1993), 133--158.

36

X. Chen, Axially symmetric jets of compressible fluids, Nonlinear Analysis 16 (1991), 1057--1087.

37

X. Chen, Collision of two jets of compressible fluid in FREE BOUNDARY PROBLEM IN FLUID FLOW WITH APPLICATIONS, J.M. Chadam & H. Rasumuseen, eds., Pitman Research Notes in Mathematics Ser. 282 (1993), 2--7.

38

X. Chen and A. Friedman, A nonlocal diffusion equation arising in terminally attached polymer chains, European J. Appl. Math. 1 (1990), 311--326.

39

X. Chen, A. Friedman, and T. Kimura, Nonstationary filtration in partially saturated porous media, European J. Math. Appl. Anal. 5 (1994), 405--429.

40

X. Chen and R. Ore, Electro-optic modulation in an arbitrary cross-section waveguide, IEEE, J. Quantum Electronics 26 (1990), 532--540.

41

X. Chen and A. Friedman, Maxwell's equations in a periodic structure, Trans. Amer. Math. Soc. 323 (1991), 465--507.

42

X. Chen, A. Friedman, and L.S. Jiang) Mathematical modeling of semiconductor lasers, SIAM J. Appl. Math. 53 (1993), 168--186.

43

D.P. Chock, S.L. Winkler and P. Sun, A comparison of stiff chemistry solvers for air quality modeling, Environmental Science & Technology 28, No. 11 (1994), 1882--1892.

44

D.C. Dobson, A boundary determination problem from the design of diffractive periodic structures, in Free boundary problems: theory and applications, J.I. Diaz, M.A. Herrero, A. Li\~{n}an, and J.L. Vazquez, eds., Pitman Research N otes in Math. Series 323, Longman (1995), 108--120.

45

D.C. Dobson, A variational method for electromagnetic diffraction in biperiodic structures, RAIRO, Mod\'{e}l, Math. Anal. Num\'{e}r 28 (1994), 419--439.

46

D.C. Dobson, Controlled scattering of light waves: optimal design of diffractive optics, in Control problems in industry, I. Lasiecka and B. Morton, eds., Birkh\"{a}user, Boston (1995), 97--118.

47

D.C. Dobson, Designing periodic structure with specified low frequency scattered far field data, in ``Advances in computer methods for partial differential equations VII, '' edited by R. Vichnevetsky, D. Knight and G. Richter, IMAC S (1992), 224--230.

48

D.C. Dobson, Optimal design of periodic antireflective structures for the Helmholtz equation, European J. Appl. Math. 4 (1993), 321--340.

49

D.C. Dobson, Phase reconstruction via nonlinear least-squares, Inverse Problems 8 (1992), 541--557.

50

D.C. Dobson, Optimal shape design of blazed diffraction gratings, Appl. Math. Opt., to appear.

51

D.C. Dobson and J.A. Cox, Mathematical modeling for diffractive optics, in Diffractive and miniaturized optics, S. Lee.,ed., SPIE CR-49 (1994), 32--53.

52

D.C. Dobson, J.A. Cox, J.D. Zook, and T. Ohnstein, Optical performance of high-aspect LIGA gratings, Opt. Eng. 36 (5) (1997), 1367--1373.

53

D.C. Dobson, J.A. Cox, J.D. Zook, and T. Ohnstein, Optical performance of high-aspect LIGA gratings, in SPIE Proc. 2383A (1995).

54

D.C. Dobson and A. Friedman, The time harmonic Maxwell equations in doubly periodic structure, J. Math. Anal. Appl. 166 (1992), 507--528.

55

A. Friedman and M.L. Honig, On the spread of continuous-time linear systems, SIAM J. Math. Anal. 21 (1990), 757--770.

56

A. Friedman and B. Hu, A free boundary problem arising in electrophotography, Nonlinear Analysis 9 (1991), 729--759.

57

A. Friedman and B. Hu, A free boundary problem arising in superconductor modeling, Asymptotic Analysis 6 (1992), 109--133.

58

A. Friedman and B. Hu, A non-stationary multi-scale oscillating free boundary for the Laplace and heat equations, Journal of Differential Equations 137 (1997), 119-165.

59

A. Friedman and B. Hu, A Stefan problem for multi-dimensional reaction diffusion systems, SIAM J. Math. Anal. 27 (1996).

60

A. Friedman and B. Hu, Head-media interaction in magnetic recording, Archive Rat. Mech. Anal.

61

A. Friedman and B. Hu, Homogenization approach to light scattering from polymer-dispersed liquid crystal film, SIAM J. Appl. Math. 52 (1992), 46--54.

62

A. Friedman and B. Hu, Optimal control of chemical vapor deposition reactor, Journal of Optimization Theory and Applications.

63

A. Friedman and B. Hu, The Stefan problem with kinetic condition at the free boundary, Scuol. Norm. Sup. Pisa. 19 (1992), 615--636.

64

A. Friedman, B. Hu, and Y. Liu, A boundary value problem for the Poisson equation with multi-scale oscillating boundary, Journal of Differential Equation 137 (1997), 54--93.

65

A. Friedman and C. Huang, Averaged motion of charged particles in a curved strip, SIAM J. Appl. Math.

66

A. Friedman and C. Huang, Averaged motion of charged particles under their self-induced field, Indiana University Mathematical Journal 43 (1994), 1167--1225.

67

A. Friedman, C. Huang and J. Yong, Effective permeability of the boundary of a domain, Comm PDE. 20 (1995), 59--102.

68

A. Friedman and W. Liu, A system of partial differential equations arising in electrophotography 89 (1991), 272--304.

69

A. Friedman and Y. Liu, Propagation of cracks in elastic media, Archive Rat. Mech. Anal. 136 (1996), 235--290.

70

A. Friedman and B. Ou, A Model of crystal precipitation, J. Math. Anal. Appl. 137 (1989), 550--575.

71

A. Friedman, B. Ou, and D. Ross, Crystal precipitation with discrete initial data, J. Math. Anal. Appl. 137 (1989), 576--590.

72

A. Friedman and F. Reitich, A hyperbolic inverse problem arising in the evolution of combustion aerosol, Archive Rat. Mech. Anal. 110 (1990), 313--350.

73

A. Friedman and F. Reitich, Asymptotic behavior of solutions of coagulation-fragmentation models, submitted to Indiana Univ. Math. J. (1997).

74

A. Friedman and F. Reitich, Parameter identification in reaction diffusion models, Inverse Problems 8 (1992), 187--192.

75

A. Friedman, D.S. Ross, and J. Zhang, A Stefan problem for a reaction diffusion system, SIAM J. Math. Analysis 26 (1995), 1089--1112.

76

A. Friedman and G. Rossi, Phenomenological continuum equations to describe case II diffusion in polymetric materials, Macromolecules, 30 (1997), 153--154.

77

A. Friedman and J.J.L. Vel\'{a}zquez, A time-dependent free boundary problem modeling the visual image in electrophotography, Arch. Rat. Mech. Anal. 123 (1993), 259--303.

78

A. Friedman and J.J.L. Vel\'{a}zquez, Liouville type theorems for fourth order elliptic equations in a half-space, Transactions Amer. Math. Soc. 349 (1997), 2537--2603.

79

A. Friedman and J.J.L. Vel\'{a}zquez, The analysis of coating flows in a strip, J. Diff. Eqs. 121 (1995), 134--182.

80

A. Friedman and J.J.L. Vel\'{a}zquez, The analysis of coating flows near the contact line, J. Diff. Eqs. 119 (1995), 137-208. in electrophotography, Arch. Rat. Mech. Anal. 123 (1993), 259--303.

81

A. Friedman and J.J.L. Vel\'{a}zquez, Time-dependent coating flows in a strip, Part I: the linearized problem Transactions Amer. Math. Soc. 349 (1997), 2981--3074.

82

A. Friedman and J. Zhang, Swelling of a rubber ball in the presence of good solvent, Nonlinear Analysis 25 (1995), 547--568.

83

B. Hu, A fiber tapering problem, Nonlinear Analysis: Theory, method an application 15, No. 6 (1990), 513--525.

84

B. Hu, A free boundary problem for a Hamilton Jacobi equation arising in ion etching, Journal of Differential equation 86, No. 1 (1990), 158--182.

85

B. Hu, A quasi-variational inequality arising in elastohydrodynamics, SIAM J. Math. Anal. 21, No. 1 (1990), 18--36.

86

B. Hu, Diffusion of penetrant in a polymer: a free boundary problem, SIAM J. Math. Anal. 22, No. 4 (1991), 934--956.

87

B. Hu and Lihe Wang, A free boundary problem arising in electrophotography: solutions with connected toner region, SIAM J.. Math. Anal. 23, No. 6 (1992), 87--111.

88

B. Hu and L. Wang, A free boundary problem arising in electrophotography: solutions with connected toner region, SIAM J. Appl. Math. 23 (1992), 1439--1454.

89

W. Liu, A parabolic system arising in film development, IMA Preprint Series # 577 (1989).

90

Y. Liu, Axially symmetric jet flows arising from high speed fiber coating in Nonlinear Analysis, Nonlinear Anal., Theory, Methods \& Applications, An international Multidisciplinary J. 23 (1994), No. 3, 319--363.

91

B. Morton and M. Elgersma, A new computational algorithm for 7R spatial mechanisms, Mech. Mach. Theory 31 (1996), 24--43.

92

C.P. Please and D.W. Schwendeman, Light-off behavior of catalytic converter, SIAM J. Appl. Math. 54 (1994), 72--92.

93

F. Reitich, Rapidly stretching plastic jets: The linearized problem, SIAM J. Math. Anal 22 (1991), 107--128.

94

F. Reitich, Singular solutions of a transmission problem in plane linear elasticity for wedgeshaped regions, Numer. Math. 59 (1991), 179--216.

95

F. Reitich and K. Ito, A high-order perturbation approach to profile reconstruction. I: perfectly conducting gratings, submitted (1997).

96

A. Solomonoff, Fast algorithms for micromagnetic computations, IMA Preprint Series # 1176 (1993).

97

P. Sun, D.P. Chock and S.L. Winkler, An implicit-explicit hybrid solver for a system of stiff kinetic equations, Journal of Computational Physics 115, No. 2 (December 1994), 515--523.

98

L. Wang, J.A. Cox, and A. Friedman, Model analysis of homogeneous optical waveguides by boundary integral method, IMA Preprint Series # 1457, February 1997.

99

T.H. Whitesides and D. Ross, Experimental and theoretical analysis of the limited coalescence process: stepwise limited coalescence, J. Colloid and Interface Science 196 (1995), 48--59.

100

J. Zhang, A nonlinear multi-dimensional conservation law, J. Math. Anal. Appl. 204 (1996), 353--388.