WELCOME - BIENVENUE

 
  
     
Toka Diagana
 Professor

CAMPUS MAILING ADDRESS

Department of Mathematics
Howard University
2441 6th Street NW
Washington, DC 20059
USA
Phone: (202) 806-7123
Fax: (202) 806-6831
E-mail: tdiagana@howard.edu

 

GRADUATE COURSE                                                                                                                                                                                                                                                                                                                                                                        

Semester: Fall 2011

  • Course Name: Partial Differential Equations II
  • Office Hours: TBA
  • Location: ASB-B, Room 213
  • Syllabus: Click here
  • Textbooks:

     -  "An Introduction to Partial Differential Equations" By Michael Renardy and Robert C. Rogers. Texts in Applied Mathematics 13, Springer-Veralg, 1993.

          - "Partial Differential Equations" by Lawrence C. Evans. AMS, Graduate Studies in Mathematics 19, 1998.

  • Course Outline

- Banach and Hilbert Spaces (Lp, Sobolev spaces, Holder spaces, Projection Theorem, Lax-Milgram Theorem, etc)

- Elements of Functional Analysis (Bounded and Unbounded Operators, Semigroups, Evolution Families, Evolution Equations...etc)

- Distributions and Fundamental Solutions to PDEs–Fourier Transform

- Second-Order Elliptic Equations

- Variational Formulation of Boundary Value Problems

- The Maximum Principles

- Representation of Solutions to PDEs (Cole-Hopf Transform, ... etc)

- The Calculus of Variations – Nonlinear PDEs

- Hamilton-Jacobi Equations

- Systems of Conservation Laws

 

Semester: Spring 2011

  • Course Name: Partial Differential Equations I
  • Office Hours: MF 2:15-3:15 and W 11:00-12:00
  • Location: ASB-B, Room 213
  • Textbook: "Beginning Partial Differential Equations" by Peter V. O'Neil, Second Edition, WILEY, 2008
  • Syllabus: Click here
  • HOMEWORK 1 (Due February 11, 2011)
  • HOMEWORK 2 (Due February 28, 2011)
  • HOMEWORK 3 (Due March 21, 2011)
  • HOMEWORK 4 (Due April 22, 2011
  •                                                                                                                                                                                                                                            

RESEARCH AREAS AND CURRENT RESEARCH INTERESTS

 
Abstract Differential Equations
  • Functional Differential Equations
  • Integrodifferential Equations
  • Stochastic Differential Equations
  • Difference Equations
  • Operator Theory
  • p-adic Functional Analysis.
 
Research Interests: Most interesting phenomena encountered in our daily life can be described through differential equations. In recent years, my goal has been to study the existence of solutions to abstract differential equations in various classes of functions such as almost periodic functions, almost automorphic functions, pseudo almost periodic functions, pseudo almost automorphic functions as well as weighted pseudo almost periodic functions we recently introduced in the literature. One of my current goals consists of studying singular, stochastic and fractional (higher-order) differential equations in connection with the above-mentioned classes of functions.

It is well-known that the best way to understand properties of linear operators is through their spectral analysis. In particular, the spectral theory for linear operators plays a crucial role in several fields including quantum mechanics. Except for a few investigations such as the pioneer work of Vishik, there is no general spectral theory for linear operators in the non-archimedean setting. One of my current goals consists of developing a general spectral theory for unbounded linear operators on non-archimedean Banach spaces.

    PROFESSIONAL EXPERIENCE

    • Professor (Howard University, 2007-Present)
    • Associate Professor (Howard University, 2004-2007)
    • Assistant Professor (Howard University, 2002-2004)
    • Lecturer (Howard University, 2000-2002)
    • ATER (A Temporarary Teaching and Research Position), Université Claude Bernard - Lyon 1, France
    • Instructor at Collège Jean Jaurés, Villeurbanne, France
    • Instructor at Collège de Thoissey, L'Ain, France

    EDUCATION

    BOOKS

    (With P. H. Bezandry)  ALMOST PERIODIC STOCHASTIC PROCESSES. Springer, New York - April, 2011.
     
     

     

    PSEUDO ALMOST PERIODIC FUNCTIONS IN BANACH SPACES. Nova Science Publishers, New York, 2007.

     

     
     
     
     
    NON-ARCHIMEDEAN LINEAR OPERATORS AND APPLICATIONS. Nova Science Publishers, New York, 2006.
     
     

    SELECTED PUBLICATIONS (2008-2011)  ----- DIAGANA HAS AUTHORED OVER 100 PUBLICATIONS (ARTICLES) AND FOUR MONOGRAPHS

     

    1. Diagana, Toka: Existence of Almost Periodic Solutions to Some Third-Order Nonautonomous Differential Equations. E. J. Qualitative Theory of Diff. Equ. No. 66 (2011), pp. 1-12.
    2. Diagana, Toka: Doubly-Weighted Pseudo Almost Periodic Functions. Afr Diaspora J. Math. Special Volume in Honor of Profs. C. Corduneanu, A. Fink, and S. Zaidman. Vol. 12 (2011), no. 1, pp. 121-136.
    3. Diagana, Toka:  Almost Periodic Solutions For Some Higher-Order Nonautonomous Differential Equations with Operator Coefficients. Mathematical and Computer Modelling. (in press). June, 2011.
    4. Diagana, Toka: Pseudo Almost Periodic Solutions for Some Classes of Nonautonomous Partial Evolution Equations. Journal of the Franklin Institute. (in press). May, 2011.
    5. Diagana, Toka: Existence of a Weighted Mean for Almost Periodic Functions. Nonlinear Analysis Series A: Theory, Methods & Applications. (in press). April, 2011.
    6. Diagana, Toka: Existence of Pseudo Almost Automorphic Solutions to a Nonautonomous Heat Equation. Cubo. Vol. 13 (2011), no. 1, pp. 67-95.
    7. Diagana, Toka: Bounded Solutions to Some Classes of Nonautonomous Higher-Order Differential Equations. Afrika Matematika (in press). February, 2011.
    8. Diagana, Toka: Existence of Pseudo Almost Automorphic Mild Solutions to Some Nonautonomous Second-Order Differential Equations. Rocky Mountain Journal of Mathematics (in press). February, 2011.
    9. Diagana, Toka: Almost Periodic Solutions to Some Second-Order Nonautonomous Differential Equations. Proceedings of the American Mathematical Society (in press). December, 2010.
    10. Diagana, Toka: Existence of Doubly-Weighted Pseudo-Almost Periodic Solutions to Some Classes of Nonautonomous Differential Equations. Electronic Journal of Differential Equations. Vol. 2011 (2011), No. 28, pp. 1-15.
    11. Diagana, Toka; Existence of Pseudo Almost Automorphic Mild Solutions to Some Nonautonomous Partial Evolution Equations. Advances in Difference Equations.Volume 2011, Article ID 895079, 23 pages. doi:10.1155/2011/895079.
    12. (BOOK) Diagana, Toka (with P. H. Bezandry); Almost Periodic Stochastic Processes. 250 pages. Springer. October, 2010.
    13. Diagana, Toka (with P. H. Bezandry);  Square-Mean Almost Periodic Solutions to Some Classes of Nonautonomous Stochastic Evolution Equations With Finite Delay. Journal of Applied Functional Analysis (in press). October, 2010.
    14. Diagana, Toka; Almost Automorphic Mild Solutions to Some Classes of Nonautonomous Higher-Order Differential Equations. Semigroup Forum (in press).  September, 2010.
    15. Diagana, Toka; Existence of Weighted Pseudo-Almost Periodic Solutions to Some Classes of Nonautonomous Partial Evolution Equations. Nonlinear Analysis (in press).  September, 2010.
    16. Diagana, Toka (with G. M. Mophou and G. M. N'Guérékata) On the existence of mild solutions to some semilinear fractional integro-differential equations. E. J. Qualitative Theory of Diff. Equ., No. 58. (2010), pp. 1-17.
    17. Diagana, Toka (with Attimu Dodzi) Representation of Bilinear Forms by Linear Operators In Non-Archimedean Hilbert Space Equipped with a Krull Valuation. Rendiconti Seminario Matematico Università e Politecnico di Torino. Vol. 68 (2010), no. 2, pp. 139-159.
    18. Diagana, Toka (with P. H. Bezandry) Existence of square-mean almost periodic mild solutions to some nonautonomous stochastic second-order differential equations, Electronic Journal of Differential Equations. Vol. 2010(2010), No. 124, pp. 1-25.
    19. Diagana, Toka; Existence of Almost Automorphic Solutions to Some Classes of Nonautonomous Higher-Order Differential Equations. Electronic Journal of Qualitative Theory of Differential Equations, No. 22 (2010), pp. 1-26.
    20. Diagana, Toka (with Paul H. Bezandry) Existence of Square-Mean Almost Periodic Solutions to Some Stochastic Hyperbolic Differential Equations with Infinite Delay. Commun. Math. Anal. 8 (2010), no. 2, pp. 103-124. (Special Issue in Honor of Prof. Peter D. Lax.)
    21. Diagana, Toka; Existence of Pseudo Almost Automorphic Solutions to a Nonautonomuous Heat Equation. Cubo: A Mathematical Journal. (2009). (in press).
    22. Diagana, Toka; Pseudo-Almost Automorphic Solutions to Some Classes of Nonautonomous Partial Evolution Equations. Differential Equations and Applications 1 (2009), no. 4, pp. 561–582.
    23. Diagana, Toka (with Paul H. Bezandry) Existence of square quadratic-mean almost periodic solutions to some stochastic hyperbolic differential equations. Electron. J. Differential Equations Vol. 2009(2009), No. 111, pp. 1-14.
    24. Diagana, Toka; Pseudo Almost Automorphic Solutions to Some Neutral Delay Integral Equations of Advanced Type. Afr. Diaspora J. Math. 8(2009), No. 2, pp. 90-99. (Special Issue in Memory of Prof. Ibni Oumar Mahamat Saleh.)
    25. Diagana, Toka (with Gisele M. Mophou and Gaston M. N'Guerekata) Existence of Weighted Pseudo Almost Periodic Solutions to Some Classes of Differential Equation with Sp-Weighted Pseudo Almost Periodic Coefficients. Nonlinear Analysis (2009). (in press).
    26. Diagana, Toka (with Ravi Agarwal) Existence of Pseudo Almost Automorphic Solutions for the Heat Equation with Sp-Pseudo Almost Automorphic Coefficients. Boundary Value Problems (2009). (in press).
    27. Diagana, Toka (with George D. McNeal); Erratum to: "Spectral Analysis for Rank One Perturbations of Diagonal Operators in Non-Archimedean Hilbert Space".Commentationes Mathematicae Univ. Carolin. (2009). (in press).
    28. Diagana, Toka (with George D. McNeal); Spectral Analysis for Rank One Perturbations of Diagonal Operators in Non-Archimedean Hilbert Space. Commentationes Mathematicae Univ. Carolin. 50(2009), no. 3, pp. 385-400.
    29. Diagana, Toka; Erratum to "Existence of Solutions to Some Classes of Partial Fractional Differential Equations". Advances in Dynamical Systems and Applications 4 (2009), no. 2, pp. 25-26.
    30. Diagana, Toka; Existence of Solutions to Some Classes of Partial Fractional Differential Equations. Nonlinear Analysis. (2009). (in press).
    31. Diagana, Toka (with Dodzi Attimu); Functional Calculus for a Class of Unbounded Linear Operators on Some Non-Archimedean Banach Spaces. Commentationes Mathematicae Univ. Carolin. 50(2009), no. 1, 37-60.
    32. Diagana, Toka; Existence of Weighted Pseudo Almost Periodic Solutions to Some Classes of Hyperbolic Evolution Equations. J. Math. Anal. Appl. 350 (2009), Issue 1, Pages 18-28.
    33. Diagana, Toka (with M. Baroun; S. Boulite; and L. Maniar); Almost Periodic Solutions to Some Semilinear Nonautonomous Thermoelastic Plate Equations. J. Math. Anal. Appl. 349 (2009), Issue 1, Pages 74-84.
    34. Diagana, Toka (with E. Hernandez and J. P. C. dos Santos); Existence of Asymptotically Almost Automorphic Solutions to Some Abstract Partial Neutral Integro-Differential Equations. Nonlinear Analysis (2008). (in press).
    35. Diagana, Toka (with P. H. Bezandry); Existence of S2-Almost Periodic Solutions to a Class of Nonautonomous Stochastic Evolution Equations. E. J. Qualitative Theory of Diff. Equ., No. 35. (2008), pp. 1-19.
    36. Diagana, Toka; On the Existence of Almost Automorphic Solutions to Some Abstract Hyperbolic Differential Equations. Bulletin of the Belgian Mathematical Society (2008). (in press).
    37. Diagana, Toka; Existence of Almost Automorphic Solutions to Some Neutral Functional Differential Equations with Infinite Delay. Electron. J. Diff. Eqns. Vol. 2008(2008), No. 129, pp. 1-14.
    38. Diagana, Toka; Existence of Almost Automorphic Solutions to Some Partial Hyperbolic Differential Equations with Sp-Almost Automorphic Coefficients. Proceedings of the 6th International Conference on Differential Equations and Dynamical Systems held at Morgan State University, Maryland, May 22-26, 2008. Dynamics of Continuous, Discrete and Impulsive Systems, Series A (2008). (in press).
    39. Diagana, Toka; Existence of Pseudo Almost Automorphic Solutions to Some Abstract Differential Equations with Sp-Pseudo Almost Automorphic Coefficients. Nonlinear Anal (2008). (in press)
    40. Diagana, Toka; Weighted Pseudo Almost Periodic Solutions to Some Neutral Delay Integral Equation of Advanced Type. Nonlinear Anal. 70 (2009), Issue 1, Pages 298-304.
    41. Diagana, Toka; Stepanov-like Pseudo Almost Periodicity and Its Applications to Some Nonautonmous Differential Equations. Nonlinear Anal. 69 (2009), Issue 12, Pages 4277-4285.
    42. Diagana, Toka; Henriquez, Hernan R.; and Hernandez M., Eduardo; Asymptotically Almost Periodic Solutions to Some Classes of Second-Order Functional Differential Equations. Differential and Integral Equations 21 (2008), nos. 5-6, 575-600.
    43. Diagana, Toka; Henriquez, Hernan R.; and Hernandez M., Eduardo, Almost Automorphic Solutions to Some Partial Neutral Functional Differential Equations. Nonlinear Anal. 69 (2008), 1485-1493.
    44. Diagana, Toka; Existence of weighted pseudo almost periodic solutions to some non-autonomous differential equations. Int. J. Evol. Equ. 2 (2008), no. 4, 397--410. (MR2403848)
    45. Diagana, Toka; Weighted pseudo-almost periodic solutions to some differential equations. Nonlinear Anal. 68 (2008), no. 8, 2250--2260. (MR2398647)
    46. Bezandry, Paul H.; Diagana, Toka; Elaydi, Saber; On the stochastic Beverton-Holt equation with survival rates. J. Difference Equ. Appl. 14 (2008), no. 2, 175--190. (MR2383001)

    AWARDS, PRIZES, AND MEMBERSHIP

    • THE AFRICAN ACADEMY OF SCIENCES Membership (Elected in November, 2009)
    • EMERGING SCHOLAR AWARD (Howard University, April, 2006)
    • CHINGUITT PRIZE IN SCIENCES (December, 2006)

    PhD DIRECTED

    • Sandra Farrier, Howard University, Department of Mathematics, January 2005

      Thesis:"Fixed-Point and Ergodic Theorems for Nonexpansive Mappings on Ultrametric Banach Spaces"

    • Dodzi Attimu, Howard University, Department of Mathematics, February 2008

      Thesis: "Linear Operators on Some Non-Archimedean Hilbert Spaces and Their Spectral Theory"

    • Najja Al-Islam, Howard University, Department of Mathematics, January 2009

      Thesis: "Pseudo Almost Periodic Solutions to Some Systems of Nonlinear Hyperbolic Second-Order Partial Differential Equations"

    • George D. McNeal, Howard University, Department of Mathematics, November 2009

      Thesis: "Spectral Analysis for Rank-One Perturbations of Diagonal Operators in Non-Archimedean Hilbert Space"

    PROFESSIONAL COMMITTEES/PANELS

    • IBNI OUMAR MAHAMAT SALEH Prize Panel (2009-present)
    • The American Mathematical Society "COMMITTEE ON HUMAN RIGHTS OF MATHEMATICIANS" (2011-2014)
    • The Amercian Mathematical Society "BOOKS AND JOURNAL DONATIONS STEERING COMMITTEE" (2010-2013)

       

    EDITORSHIP

    LINKS

     

    NON-MATHEMATICAL ARTICLES