CURRICULUM VITAE

Jerry Bebernes

PERSONAL:

Professor of Applied Mathematics
University of Colorado, Boulder

Address: Department of Applied Mathematics
526 UCB
University of Colorado
Boulder   CO   80309-0526

Telephone: Office: 303-492-7563
Home: 303-499-9053
Email: bebernes@colorado.edu

 

EDUCATION:

Ph.D.
M.A.
B.S. 		University of Nebraska, Mathematics
University of Nebraska, Mathematics
University of Nebraska, Mathematics 		1962
1959
1957

 

PROFESSIONAL EXPERIENCE:

 

LONG TERM POSITIONS:

           

                        Instructor                     University of Nebraska                       1959-62

                        Assistant Professor     University of Colorado                        1962-67

                        Associate Professor     University of Colorado                        1967-71

                        Professor                     University of Colorado                        1971-

 

VISITING POSITIONS AND FELLOWSHIPS:

 

                        Graduate Fellowship   National Science Foundation               1961

                        Faculty Fellowship      University of Colorado                        1969-70

Spent academic year at Istituto

Matmatico “Ulisse Dini”

Florence, Italy

                        CNR Fellowship         Universita di Firenze                           Summer 1970

                        Visiting Professor       University of Utah                               1971-1972

                        Visiting Professor       Universita di Padova                            Jan.-April 1980

                        Visiting Professor       Catholique Universite                          May-June 1980

                                                            Louvain-la-Neuve, Belgium

Visiting Professor       CNR 9th Summer School of                September 1984

                                    Mathematical Physics

                                    Ravello, Italy

                        Visiting Professor       University of Wyoming                      Jan -May 1986

                        Faculty Fellowship      University of Colorado                        1986-1987

                        Visiting Professor       Brigham Young University                  March 1987

 

Visiting Professor       Catholique Universite                          April-May 1987

                                                            Louvain-la-Neuve, Belgium                

                        Visiting Professor       Heriott-Watt University                       May 1988

                                                            Edinburgh, Scotland

                        Visiting Professor       SISSA, Trieste, Italy                            April-May 2000

 

ADMINISTATIVE POSITIONS AND PROFESSIONAL SERVICE:

 

                        Associate Chairman     Department of Mathematics                1967-1969

                                                            University of Colorado

 

                        Chairman of the           Mathematical Association of America 1968-1969

                        Rocky Mountain

                        Section

                        Representative             Rocky Mountain Mathematical           1976-1979/2000-2002

                        Chairman                     Consortium    

                        Editor                          Rocky Mountain Journal                     1988-2002

                                                            of Mathematics

Editor                          Communications on Applied               1996-2000

Nonlinear Analysis

                        Program Director        National Science Foundation               1991-1992

 

PROFESSIONAL PUBLICATIONS:

MONOGRAPHS:

1.   A mathematical analysis of some problems from combustion theory,
        Lecture Notes in Mathematics, CNR, Italy, 64 pages

2.   Mathematical problems from combustion theory, (with D. Eberly)
        Applied Mathematics Series, vol. 83 (1989) Springer-Verlag, New York, Inc. 177 pp.

RESEARCH PAPERS:

1.   A sub-function approach to a boundary value problem for ordinary differential equations,
        Pacific J. Math, 13 (1963) 1053-1066

2.   On the asymptotic behavior of linear differential equations (with N.X. Vinh),
        Amer. Math. Monthly, 72 (1965) 285-287

3.   Differential paths and the continuation of solutions of differential equations (with W. Fulks & G. Meisters),
        Differential Equations, 2 (1966) 102-106

4.   Differential inequalities with countable exceptional sets (with G.H. Meisters),
        J. Differential Equations, 2 (1966) 391-398

5.   An elementary proof of some differential inequalities (with G.H. Meisters),
        J.Math. Anal. Appl., 17 (1967) 92-98

6.   Infinite interval boundary value problems for   y'=f(x,y)   (with L.K.Jackson),
        Duke Math. J., 34 (1967) 39-47

7.   A generalized two-point boundary value problem (with Robert Gaines),
        Proc.Amer. Math. Soc., 19 (1968) 749-754

8.   Dependence on boundary date and a generalized boundary value problem (with Robert Gaines),
        J. Differential Equations, 4 (1968) 359-368

9.   A technique for solving two-dimensional boundary value problems (with Russell Wilhelmsen),
        SIAM J. Appl. Math., 1 (1969) 1060-1064

10.   A technique for solving two-dimensional boundary value problems (with Russell Wilhelmsen),
        Studies in Applied Mathematics 5, Society for Industrial and Applied Mathematics, (1969) 202-203

11.   A general boundary value problem technique (with Russell Wilhelmsen),
        J. Differential Equations, 8 (1970) 404-415

12.   Investigations in the topological method of Wazewski (with J.D. Schuur),
        Rend. Mat. E Appl., 49 (1970) 39-42

13.   The Wazewski topological method for contingent equations (with J.D. Schuur),
        Ann. Mat Pura Appl., 87 (1970) 271-279

14.   A remark concerning a boundary value problems (with R. Wilhelmsen),
        J. Differential Equations, 10 (1971) 389-391

15.   Existence and non-existence of maximal solutions for y"=f(x,,y,y'),
        Ann. Polon. Math., 25 (1971), 125-138

16.   A priori bounds for boundary sets (with R. Fraker),
        Proc. Amer. Math. Soc., 29 (1971) 313-318

17.   Periodic boundary value problems for systems of second order differential equations (with K. Schmitt),
        J. Differential Equations, 13 (1973) 32-47

18.   Some boundary value problems for generalized differential equations (with W. Kelley),
        SIAM J. Appl. Math., (1973) 16-23

19.   An existence theorem for periodic boundary value problems for systems of second order differential equations,
        Arch. Math. (Brno), 4 VIII (1972) 173-176

20.   A simple alternative problem for finding periodic solutions of second order ordinary differential systems,
        Proc. Amer. Math. Soc., 42 (1974) 121-127

21.   Existence of periodic solutions for third and fourth order ordinary differential equations via coincidence degree
        (with K. Schmitt & R. Gaines), Ann. Soc. Sci. Bruxxelles Ser. I, 88 (1974) 25-36

22.   Positive Invariance and Wazewski Theorem, Ordinary and Partial Differential Equations,
        Lecture Notes in Mathematics 415, Springer, (1974) 35-39

23.   Invariant sets and the Hukuhara-Kneser property for systems of parabolic partial differential equations (with K. Schmitt),
        Rocky Mountain J. Math., 7 (1977) 557-568

24.   On existence of maximal and minimal solutions for parabolic partial differential equations (with K. Schmitt),
        Proc. Amer. Math. Soc., (1979) 211-218

25.   Solution set properties for some nonlinear parabolic differential equations,
        Proceedings of Equadiff 4, Lecture Notes in Mathematics, #703, Springer-Verlag, (1979) 25-31

26.   Periodic solutions for Lienard systems (with M. Martelli),
        Boll. Unione Mat. Ital., 16-A (1979) 398-405

27.   Some applications of invariance for parabolic systems (with K.N. Chueh, W.Fulks),
        Indiana Univ. Math. J., 28 (1979) 269-277

28.   Continua of solutions for periodic boundary value problems (with M. Martelli),
        Journal of Nonlinear Analysis: Theory, Methods, and Applications, 4 (1980) 821-830

29.   A mathematical analysis of blow up for thermal reactions – the spatially nonhomogeneous case (with D. Kassoy),
        Siam J. Appl. Math., 40 (1981) 476-484

30.   Thermal behavior for a confined reactive gas (with A. Bressan),
        J. Differential Equations, 44 (1982) 118-133

31.   Comparison techniques and the method of lines for a parabolic functional Equation (with R. Ely),
        Rocky Mountain J. Math., 12 (1982) 723-733

32.   Ignition for a gaseous thermal reaction,
        Proceedings of Equadiff 5, Teubner Text, 1982, Band 47, M. Gregus, Editor, 34-36

33.   Self-ignition for thermal reactions, Transactions of the twenty-seventh conference of Army mathematicians,
        ARO Report 82-1, 687-706

34.   Existence and invariance for parabolic functional equations (with R. Ely),
        Nonlinear Analysis: Theory, Methods, and Applications, 7 (1983) 1225-1236

35.   The small heat-loss problem, (with W. Fulks),
        J. Differential Equations, 56 (1985) 324-332

36.   Global a priori estimates for the solution of the initial boundary value problem for a viscous reactive gas (with A. Bressan),
        Proceedings Royal Soc. Edinburgh, 101A (1985) 321-333

37.   Solution profiles for some simple combustion models (with D Eberly & W. Fulks),
        J. Nonlinear Analysis: Theory, Methods & Applications, 10 (1986) 165-177

38.   Solid fuel combustion—some mathematical problems,
        Rocky Mountain Journal of Mathematics, 16 (1986) 417-433

39.   Solution profiles an thermal runaway (with D. Kassoy),
        Lectures in Applied Mathematics, 24 (1986) 217-228

40.   A description of blow-up for the solid fuel ignition model, Proceedings of Equadiff 6,
        Springer-Verlag (1985) 193-197

41.   Nonexistence for the Kassoy problem (with W. Troy),
        SIAM J. Math Anal., 18 (1987) 1157-1162

42.   Existence for the modified Kassoy problem (with W. Troy),
        Proceedings Royal Soc. Edinburgh 106A (1987) 131-136

43.   An asymptotic description of blow-up (with A. Bressan & D. Eberly)
        Indiana Univ. J. Math., 36 (1987) 295-305

44.   Characterizing self-similar blowup, Mathematical Modeling in Combustion & Related Topics ,
        NATO ASI Series 140, C.M. Brauner and Cl. Schmidt-Lairé, eds., Martinus Nijhoff (1988), 383-392

45.   A Description of self-similar blow-up for dimensions n ≥ 3, (with D.Eberly).
        Ann. Inst. Henri Poincare, Analyse Nonlineare, 5 (1988) 1-21

46.   Total blow-up versus single point blow-up (with A. Bressan & A. Lacey),
        Differential Euqations, 73 (1988) 30-44

47.   Characterization of blowup for a semilinear heat equation with convection (with D. Eberly),
        Quart. J. Mech. Appl. Math., 42 (1989) 447-456

48.   Blowup---when, where, and how?,
        Bull. Soc. Math. Belg., Ser. A. XL (1988) 3-45

49.   The confined non-diffusive thermal explosion with spatially homogeneous pressure variation
        (with D. Kassoy, N. Riley, & A. Bressan), Comb. Sci. Tech., 63 (1989) 45-62

50.   Reactive-Euler induction models (with D. Kassoy),
        Transactions Sixth Army Conference on Appl. and Computing, ARO Report 89-1, 473-482

51.   Finite time blowup for a particular parabolic system (with A. Lacey),
        SIAM J. math. Analysis, 21 (1990) 1415-1425

52.   Blowup for the Reactive-Euler model (with A. Bressan), Reaction-Diffusion Equations,
        Proceedings of Reaction-Diffusion Special Year, K.J. Brown and A.A. Lacey, editors,
        Clarendon Press, Oxford, 1990, 1-24

53.   Finite time blowup for reactive-diffusive systems, (with A. Lacey),
        J. Differential Equations, 95 (1992) 105-129

54.   Final time blowup profiles for semi-linear parabolic equations via center manifold theory, (with S. Bricher),
        SAIM J. Math. Anal., 23 (1992) 852-869

55.   Asymptotics of blowup for weakly quasilinear parabolic problems (with S. Bricher & V. Galaktionov),
        J.Nonlinear Analysis, 23 (1994) 489-514

56.   On classification of blow-up patterns for a quasilinear heat equation (with V. Galaktionov),
        Integral and Diff. Eqns., 9 (1996) 655-670

57.   On symmetric and nonsymmetric blowup for a weakly quasilinear heat equation (with A. Bressan & V. Galaktionov),
        Nonlinear Differential Equations and Applications, 3 (1996) 269-286

58.   Traveling fronts in cylinders and their stability (with C. Li & Y. Li),
        Rocky Mountain J. Math. 27 (1997) 123-150

59.   Nonlocal problems modeling shear banding (with P. Talaga),
        Communications on Appl. Nonlinear Anal., 3 (1996) 79-103

60.   Global existence and finite-time blowup for a class of nonlocal parabolic problems (with A. Lacey),
        Advances in Diff. Equations, 2 (1997) 927-953

61.   Single-point blowup for nonlocal parabolic problems, (with C. Li & P. Talaga),
        Physica D, 134 (1999) 48-60

62.   Nonlocal problems modeling the formation of shear bands,
        Proc. Eight Int. Coll. on Differential Equations, D. Bainov, Editor, VMS Press (1998) 67-71

63.   Nonlocal models of shear banding,
        Proceedings of Venice-2 Symposium on Appl. And Ind. Math., R. Spigler, Editor,
        Kluwer Publ., Kluwer Academic Publishers, 2000, 33-46

 

MISCELLANEOUS PUBLICATIONS – ABSTRACTS AND REVIEWS

1.   Differential Equations – Stability, Oscillations, Time Lags by A. Halanay, Academic Press, 1996,
        SIAM Review, 10 (1969) 93-94

2.   Nonlinear Two Point Boundary Value Problems by P. Bailey, L. Shampine, and P. Waltman.
        Mathematics in Science and Engineering, Vol. 44, Academic Press, 1968.
        Bull. Amer. Math. Soc. 75 (1969) 724-727

3.   Wazewski’s Method for Contingent Equations (Abstract),
        Notices AMS 17 (1970) 824

4.   Applications of topological methods in differential equations---introduction to special issue,
        Rocky Mountain J. Mathematics, 7 (1977) 385-388

5.   The Stability of Dynamical Systems, by J.P. LaSalle, Soc. Ind. Apl.Math.,
        Regional Conference Series in Applied Mathematics, 1979, SIAM Review, 21 (1979) 418-420

6.   Nonlinear parabolic and elliptic equations, by C.V. Pao, Plenum Press, 1992.
        Bull. Amer. Math. Soc., 32 (1995) 166-169

 

Ph.D. THESES SUPERVISED:

 

SELECTED INVITED LECTURES:

1995- European Research Conference on Local Singularities of Solutions to PDE’s, September, San Feliu, Spain

1997- Eighth International Colloquium on Differential Equations, August, Plovudiv, Bulgaria

1998- Venice-2: Symposium on Applied and Industrial Mathematics, June, Venice, Italy

1999- IMA Minisymposium – Investigation of Mathematical Combustion Models-Co-organizer, November, Minneapolis, MN

2002- Durham Mathematics Conference – Mathematics of Combustion, July, Durham, England

 

RESEARCH GRANTS:

1.   NSF Grant, Beyond Blowup, July 1, 1994-June 30, 1995, $20,000.

2.   NATO Collaborative Research Grant (with Andrew Lacey), June 1992-, $6,000.

3.   NSF Grant, Mathematical Problems from Combustion Theory, May 1, 1991-June 1994, $58,500.

4.   ARO Contract (with D. Kassoy), June 1, 1991- Aug. 30, 1992, $40,000.

5.   ARO Contract, Mathematical Analysis of Transient Gas Dynamics Phenomena,
        (co-principal investigator with D.K. Kassoy), June 1, 1988-May 31, 1991, $210,000

6.   NSF Grant – Applied Mathematics, The Mathematics of Thermal Explosion Phenomena
        (with A. Bressan), May 1, 1988-April 30, 1991, $36,356.

7.   ARO Contract, A Fundamental Mathematical Theory for the Dynamics of Combustion Processes
        (co-P.I. with D.K. Kassoy), June 1, 1985-May 31, 1988, $240,000.