Ian W. Knowles, Professor
Department of Mathematics
University of Alabama at Birmingham
Birmingham, Alabama 35294
mailto:knowles@math.uab.edu
Fax: (205) 934-9025
Telephone: (205) 934-2154

List of Publications

  1. Knowles, Ian; LaRussa, Mary A. Lavrentiev's theorem and error estimation in elliptic inverse problems. In B. M. Brown, J. Lang, I. G. Wood (Eds.) Spectral Theory, Function Spaces and Inequalities: New Techniques and Recent Trends, 91-104, Operator Theory: Advances and Applications, volume 219, Springer Birkhauser, 2012, ISBN 978-3-0348-0262-8.  PDF 
  2. Knowles, Ian; LaRussa, Mary A. Conditional well-posedness for an elliptic inverse problem. SIAM J. Appl. Math., 71(2011), 952-971.  PDF 
  3. Knowles, Ian; Wallace, Robert Wallace. Numerical differentiation, Sobolev gradients, 209-223. In J. W. Neuberger Sobolev Gradients and Differential Equations, 2nd Edition, Lecture Notes in Mathematics, 1670, Springer, Heidelberg, 2010.   PDF
  4. Knowles, Ian; Yan, Aimin. The reconstruction of groundwater parameters from head data in an unconfined aquifer. J. Comp. Appl. Math. 208 (2007), 72--81  Postscript  PDF
  5. Knowles, Ian; Teubner, Michael; Yan, Aimin; Rasser, Paul; Lee, Jong Wook. Inverse groundwater modelling in the Willunga Basin, South Australia.  Hydrogeology Journal.  15 (2007), no. 6, 1107--1118   PDF    
  6. Recent Advances in Differential Equations and Mathematical Physics.  UAB International Conference on Differential Equations and Mathematical Physics, March 29 -- April 2, 2005, University of Alabama at Birmingham. Editors N. Chernov, Y. Karpeshina, I. Knowles, R. Lewis, R. Weikard.  Contemporary Mathematics, Volume 412, American Mathematical Society,  Providence R. I. , 2006.  
  7. Brown, B. M.; Jais, M.; Knowles, I. W.  A variational approach to an elastic inverse problem.  Inverse Problems, 21 (2005), 1953--1973.  PDF.
  8. Knowles, Ian. Variational methods for ill-posed problems.  In  J. M. Neuberger  (Ed.) Variational Methods: Open Problems, Recent Progress, and Numerical Algorithms (Flagstaff, Arizona, 2002), 187--199, Contemporary Mathematics, volume 357, American Mathematical Society, Providence R. I., 2004.  Postscript PDF
  9. Knowles, Ian ; Le, Tuan;  Aimin Yan. On the recovery of multiple flow parameters from transient head data.  J. Comp. Appl. Math. 169 (2004), no. 1, 1--15.  [MR2071256]  Postscript PDF
  10. Knowles, Ian; Yan, Aimin. On the recovery of transport parameters in groundwater modelling. J. Comp. Appl. Math. 171 (2004), no. 1-2, 277--290. [MR2077209]  Postscript  PDF 
  11. Knowles, Ian W.; McCarthy, Maeve L. Isospectral membranes: a connection between shape and density, J. Phys. A: Math. Gen. 37 (2004) pp. 8103-8109.   PDF
  12. Brown, B. M.; Samko, V. S.; Knowles, I. W.;  Marletta, M. Inverse spectral problem for the Sturm-Liouville equation. Inverse Problems, 19(2003),  no. 1, 235--252. [MR1964261 (2004b:34025)].   Postscript PDF  
  13. Brown, B. M.; Knowles, I.; Weikard, R.  On the inverse resonance problem.  J. London Math. Soc. (2) 68 (2003), no. 2, 383--401 [MR1994689 (2004b:34026)].  Postscript PDF
  14. Brown, B.M.; Samko, V. S.; Knowles, I. W.; Marletta, M. A numerical procedure for the inverse Sturm-Liouville operator. In S. G. Samko, A. F. Dos Santos, and A. B. Lebre (Eds) Factorization, Singular Operators, and Related Problems, Proceedings of the conference in Honor of Prof. Litvinchuk, held on Madeira (Jan. 28--Feb. 1,  2002), Kluwer Publ. House, 2003, 55--64.  [MR2001591 (2004h:34163)]. PDF
  15. Knowles, Ian W. An inverse problem for Hamiltonian systems. J. Comp. Appl. Math., 148(2002) 99--113.  Postscript PDF DVI [MR1946190 (2003i:49062)]
  16. Knowles, Ian; Yan, Aimin. The recovery of an anisotropic conductivity in groundwater modelling.  Applicable Analysis, 81(2002) 1347--1365. [MR1956065 (2004d:35250)] Postscript PDF
  17. Knowles, Ian W. Parameter estimation in groundwater modelling. Developments in Theoretical and Applied Mechanics XXI, 415--421, 2002, Rivercross Publishing Inc., Orlando, ISBN 0-615-11944-1.  Postscript PDF DVI
  18. Knowles, Ian W. Descent methods for inverse problems. Nonlinear Analysis  47 (2001) 3235-3245.  [MR1979220  (2004d:35249)]   PDF Postscript DVI
  19. Knowles, Ian. Parameter identification for elliptic problems. J. Comp. Appl. Math. 131 (2001), 175-194. [2002c:65190]  PDF Postscript
  20. Knowles, Ian Coefficient identification in elliptic differential equations. Direct and inverse problems of mathematical physics, 149--160, Int. Soc. Anal. Appl. Comput., 5, Kluwer Acad. Publ., Dordrecht, 2000. (Reviewer: Ulrich Tautenhahn) [2001f:35419]  Postscript PDF
  21. Knowles, Ian. Uniqueness for an elliptic inverse problem. SIAM J. Appl. Math. 59 (1999) no. 4, 1356--1370.  [2000a:35252] Postscript PDF DVI
  22. Browne, P. J.; Everitt, W. N.; Knowles, I. W. Douglas Barker Sears: his work in differential equations. Quaest. Math. 22 (1999), no. 1, 1--6. [1 711 858] PDF
  23. Knowles, Ian. A variational algorithm for electrical impedance tomography. Inverse Problems 14 (1998), 1513--1525.  [99i:65127] PDF Postscript
  24. Knowles, Ian; Wallace, Robert. A variational solution for the aquifer transmissivity problem. Inverse Problems 12 (1996) no. 6, 953--963. 86-XX.  [1 421 658]  PDF Postscript
  25. Differential Equations and Mathematical Physics.  Editor:  Ian W. Knowles,  International Press of Boston Inc., 1995.
  26. Knowles, Ian; Wallace, Robert. A variational method for numerical differentiation. Numer. Math. 70 (1995) no. 1, 91--110. 65D25 (49M10) [96h:65031]   PDF Postscript DVI
  27. Haddox, Jeffery L.; Knowles, Ian; Pfister, Roswell P.; Sommers, Charnell I. Characterization of chemical gradients in the collagen gel visual chemotactic assay. Journal of Immunological Methods 171: 1-14, 1994. PDF
  28. Knowles, Ian. Asymptotics of an ordinary differential equation and the Riemann hypothesis. J. Differential Equations, 83 (1990) no. 2, 207--219 (Reviewer: Matti Jutila) 11M26 (34E99) [91b:11090]. PDF
  29. Differential equations and mathematical physics. Proceedings of the international conference held at the University of Alabama in Birmingham, Birmingham, Ala., March 3--8, 1986. Edited by I. W. Knowles and Y. Saito. Lecture Notes in Mathematics, 1285. Springer-Verlag, Berlin-New York, 1987. xvi+499 pp. ISBN: 3-540-18479-1 00A11 [88h:00004]
  30. Evans, W. Desmond; Knowles, Ian. On the extension problem for singular accretive differential operators. J. Differential Equations 63 (1986) no. 2, 264--288. (Reviewer: A. D. Wood) 47B44 (34B20 47E05) [87m:47084]. PDF
  31. Everitt, W. N.; Knowles, I. W.; Read, T. T. Limit-point and limit-circle criteria for Sturm-Liouville equations with intermittently negative principal coefficients. Proc. Roy. Soc. Edinburgh Sect. A 103 (1986), no. 3-4, 215--228. (Reviewer: Walter Eberhard) 34B20 (47E05) [87k:34028 ]. PDF
  32. Evans, W. Desmond; Knowles, Ian. On the extension problem for accretive differential operators. J. Funct. Anal. 63 (1985), no. 3, 276--298. (Reviewer: H.W. Rohde) 47E05 (34G10 47B44) [87f:47071]. PDF
  33. Knowles, Ian. On differential equations associated with Euler product expressions. Trans. Amer. Math. Soc. 289 (1985), no. 2, 545--573. (Reviewer: C. Ryavec) 11M06 (30B50 30E25) [86i:11045]  PDF Postscript
  34. Differential equations. Proceedings of the international conference held at the University of Alabama in Birmingham, Birmingham, Ala., March 21--26, 1983. Edited by Ian W. Knowles and Roger T. Lewis. North-Holland Mathematics Studies, 92. North-Holland Publishing Co., Amsterdam-New York, 1984. xx+608 pp. ISBN: 0-444-86875-5 00A11 (34-06) [86f:00016]
  35. Knowles, Ian. Integral mean value theorems and the Ganelius inequality. Proc. Roy. Soc. Edinburgh Sect. A 97 (1984), 145--150. (Reviewer: Paul R. Beesack) 26D15 (26A42) [86a:26026]. PDF
  36. Knowles, Ian. Wave equations with discontinuous coefficients and the Muntz theorem. In Qualitative Properties of Differential Equations, Proceedings of the 1984 Edmonton Conference (Eds. W. Allegretto and G. J. Butler), 222--231, Edmonton, Alberta, 1984. PDF
  37. Faierman, Melvin; Knowles, Ian. On a mixed problem for a hyperbolic equation with a discontinuity in the principal coefficients. Proc. London Math. Soc. (3) 46 (1983), no. 1, 137--166. (Reviewer: Alexander Doktor) 35L20 (35C10) [84d:35085] PDF .
  38. Knowles, Ian. Eigenvalue problems and the Riemann zeta function. II. Ordinary differential equations and operators (Dundee, 1982), 267--297, Lecture Notes in Math., 1032, Springer, Berlin-New York, 1983. (Reviewer: S. W. Graham) 11M06 [85j:11098b] PDF
  39. Knowles, Ian. Eigenvalue problems and the Riemann zeta function. Ordinary and partial differential equations (Dundee, 1982), pp. 388--405, Lecture Notes in Math., 964, Springer, Berlin-New York, 1982. (Reviewer: S. W. Graham) 11M06 [85j:11098a ] PDF
  40. Knowles, Ian; Race, David. On the correctness of boundary conditions for certain linear differential operators. Spectral theory of differential operators (Birmingham, Ala., 1981), pp. 279--287, North-Holland Math. Stud., 55, North-Holland, Amsterdam-New York, 1981. (Reviewer: Plácido Z. Táboas) 34B05 (47E05) [84f:34027] PDF
  41. Knowles, Ian. Dissipative Sturm-Liouville operators. Proc. Roy. Soc. Edinburgh Sect. A 88 (1981), no. 3-4, 329--343. (Reviewer: E. I. Glazman) 34B25 (47E05) [83b:34033]. PDF
  42. Spectral theory of differential operators. Proceedings of the Conference held at the University of Alabama, Birmingham, Ala., March 26--28, 1981. Edited by Ian W. Knowles and Roger T. Lewis. North-Holland Mathematics Studies, 55. North-Holland Publishing Co., Amsterdam-New York, 1981. xv+384 pp. ISBN: 0-444-86277-3 34-06 (47-06) [82k:34002]
  43. Faierman, M.; Knowles, I. Nonmodal eigenfunction expansions. Ordinary and partial differential equations (Proc. Sixth Conf., Univ. Dundee, Dundee, 1980), pp. 109--118, Lecture Notes in Math., 846, Springer, Berlin, 1981. (Reviewer: Volker Vogelsang) 35P10 (35L05) [82j:35112] PDF
  44. Knowles, I.; Meidan, R. On nonlinear nuclear operators. J. Math. Anal. Appl. 79 (1981), no. 2, 521--535. (Reviewer: M. Edelstein) 47H99 (60G99) [82i:47103] PDF
  45. Knowles, Ian. On the boundary conditions characterizing J-selfadjoint extensions of J-symmetric operators. J. Differential Equations 40 (1981), no. 2, 193--216. (Reviewer: Björn Textorius) 47B50 (34B05) [82i:47052]. PDF
  46. Faierman, M.; Knowles, I. Minimal operators for Schrödinger-type differential expressions with discontinuous principal coefficients. Canad. J. Math. 32 (1980), no. 6, 1423--1437. (Reviewer: T. Kato) 35J10 (47F05 81C05) [82h:35022]. PDF
  47. Knowles, Ian; Race, David. On the point spectra of complex Sturm-Liouville operators. Proc. Roy. Soc. Edinburgh Sect. A 85 (1980), no. 3-4, 263--289. (Reviewer: Walter Eberhard) 34B25 (47E05) [81f:34028] PDF
  48. Knowles, Ian . On J-selfadjoint extensions of J-symmetric operators. Proc. Amer. Math. Soc. 79 (1980), no. 1, 42--44. (Reviewer: Lawrence Williams) 47B25 (47B50) [81b:47036] Postscript PDF
  49. Knowles, Ian. On stability conditions for second-order linear differential equations. J. Differential Equations 34 (1979), no. 2, 179--203. (Reviewer: E. K. H. Hoehn) 34D20 (34C11) [80j:34058]. PDF
  50. Knowles, Ian. On essential selfadjointness for Schrödinger operators with wildly oscillating potentials. J. Math. Anal. Appl. 66 (1978), no. 3, 574--585. (Reviewer: Gheorghe Nenciu) 35P05 [80f:35090] PDF
  51. Knowles, Ian. On the existence of minimal operators for Schrödinger-type differential expressions. Math. Ann. 233 (1978), no. 3, 221--227. (Reviewer: S. T. Kuroda) 35P05 (35J10) [80d:35115] PDF
  52. Knowles, Ian. On the location of eigenvalues of second-order linear differential operators. Proc. Roy. Soc. Edinburgh Sect. A 80 (1978), no. 1-2, 15--22. (Reviewer: S. J. Lee) 34B25 [80d:34026]. PDF
  53. Knowles, Ian. On the number of L2solutions of second order linear differential equations. Proc. Roy. Soc. Edinburgh Sect. A 80 (1978), no. 1-2, 1--13. (Reviewer: S. J. Lee) 34B20 [80a:34017]. PDF
  54. Knowles, Ian. On essential self-adjointness for singular elliptic differential operators. Math. Ann. 227 (1977), no. 2, 155--172. (Reviewer: Christian G. Simader) 35P05 [55 #13094]. PDF
  55. Knowles, Ian. On the number of zeros of solutions of a second-order linear differential equation. Quart. J. Math. Oxford Ser. (2) 26 (1975), no. 104, 507--510. (Reviewer: Stanley B. Eliason) 34C10 [52#14466]. PDF
  56. Knowles, Ian. On the self-adjointness of singular Sturm-Liouville operators. In Proceedings of a Symposium on Differential Equations (in honour of F. John), CSIR Wisk 161, Pretoria, 1975. PDF
  57. Knowles, Ian. On second-order differential operators of limit-circle type. Ordinary and partial differential equations (Proc. Conf., Univ. Dundee, Dundee, 1974), pp. 184--187. Lecture Notes in Math., Vol. 415, Springer, Berlin, 1974. (Reviewer: K. R. Schneider) 34B20 [54 #13194]. PDF
  58. Knowles, Ian. A limit-point criterion for a second-order linear differential operator. J. London Math. Soc. (2) 8 (1974), 719--727. (Reviewer: William N. Everitt) 34B20 [51#3597]  PDF 
  59. Knowles, Ian. Some remarks on a limit-point condition. Bull. London Math. Soc. 6 (1974), 325--332. (Reviewer: J. W. Heidel) 34B20 [50 #13702]  PDF  
  60. Knowles, Ian. On the limit-point classification of the Sturm-Liouville operator. In Proceedings of a Symposium on Differential Equations (in honour of K. O. Friedrichs), 65--80, CSIR Wisk 149, Pretoria, 1974. PDF
  61. Knowles, Ian. On a limit-circle criterion for second-order differential operators. Quart. J. Math. Oxford Ser. (2) 24 (1973), 451--455. (Reviewer: R. R. D. Kemp) 34B20 [52 #14442]. PDF
  62. Knowles, Ian. Note on a limit-point criterion. Proc. Amer. Math. Soc. 41 (1973), 117--119. (Reviewer: J. V. Baxley) 34B20 [47 #8964].   Postscript  PDF

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