



Toka Diagana
Professor

CAMPUS MAILING ADDRESS
 Department of Mathematics
Howard University 2441 6th Street NW Washington, DC 20059 USA 
Phone: 
(202) 8067123 
Fax: 
(202) 8066831 
Email: 
tdiagana@howard.edu  
GRADUATE COURSE
Semester: Fall 2011
 "Partial Differential Equations" by Lawrence C. Evans. AMS, Graduate Studies in Mathematics 19, 1998.
 Banach and Hilbert Spaces (Lp, Sobolev spaces, Holder spaces, Projection Theorem, LaxMilgram Theorem, etc)
 Elements of Functional Analysis (Bounded and Unbounded Operators, Semigroups, Evolution Families, Evolution Equations...etc)
 Distributions and Fundamental Solutions to PDEs–Fourier Transform
 SecondOrder Elliptic Equations
 Variational Formulation of Boundary Value Problems
 The Maximum Principles
 Representation of Solutions to PDEs (ColeHopf Transform, ... etc)
 The Calculus of Variations – Nonlinear PDEs
 HamiltonJacobi Equations
 Systems of Conservation Laws
Semester: Spring 2011
 Course Name: Partial Differential Equations I
 Office Hours: MF 2:153:15 and W 11:0012:00
 Location: ASBB, 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
 padic 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 (higherorder) differential equations in connection with the abovementioned classes of functions.
It is wellknown 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 nonarchimedean setting. One of my current goals consists of developing a general spectral theory for unbounded linear operators on nonarchimedean Banach spaces.
PROFESSIONAL EXPERIENCE
 Professor (Howard University, 2007Present)
 Associate Professor (Howard University, 20042007)
 Assistant Professor (Howard University, 20022004)
 Lecturer (Howard University, 20002002)
 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
SELECTED PUBLICATIONS (20082011)  DIAGANA HAS AUTHORED OVER 100 PUBLICATIONS (ARTICLES) AND FOUR MONOGRAPHS
 Diagana, Toka: Existence of Almost Periodic Solutions to Some ThirdOrder Nonautonomous Differential Equations. E. J. Qualitative Theory of Diff. Equ. No. 66 (2011), pp. 112.
 Diagana, Toka: DoublyWeighted 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. 121136.
 Diagana, Toka: Almost Periodic Solutions For Some HigherOrder Nonautonomous Differential Equations with Operator Coefficients. Mathematical and Computer Modelling. (in press). June, 2011.
 Diagana, Toka: Pseudo Almost Periodic Solutions for Some Classes of Nonautonomous Partial Evolution Equations. Journal of the Franklin Institute. (in press). May, 2011.
 Diagana, Toka: Existence of a Weighted Mean for Almost Periodic Functions. Nonlinear Analysis Series A: Theory, Methods & Applications. (in press). April, 2011.
 Diagana, Toka: Existence of Pseudo Almost Automorphic Solutions to a Nonautonomous Heat Equation. Cubo. Vol. 13 (2011), no. 1, pp. 6795.
 Diagana, Toka: Bounded Solutions to Some Classes of Nonautonomous HigherOrder Differential Equations. Afrika Matematika (in press). February, 2011.
 Diagana, Toka: Existence of Pseudo Almost Automorphic Mild Solutions to Some Nonautonomous SecondOrder Differential Equations. Rocky Mountain Journal of Mathematics (in press). February, 2011.
 Diagana, Toka: Almost Periodic Solutions to Some SecondOrder Nonautonomous Differential Equations. Proceedings of the American Mathematical Society (in press). December, 2010.
 Diagana, Toka: Existence of DoublyWeighted PseudoAlmost Periodic Solutions to Some Classes of Nonautonomous Differential Equations. Electronic Journal of Differential Equations. Vol. 2011 (2011), No. 28, pp. 115.
 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.
 (BOOK) Diagana, Toka (with P. H. Bezandry); Almost Periodic Stochastic Processes. 250 pages. Springer. October, 2010.
 Diagana, Toka (with P. H. Bezandry); SquareMean Almost Periodic Solutions to Some Classes of Nonautonomous Stochastic Evolution Equations With Finite Delay. Journal of Applied Functional Analysis (in press). October, 2010.
 Diagana, Toka; Almost Automorphic Mild Solutions to Some Classes of Nonautonomous HigherOrder Differential Equations. Semigroup Forum (in press). September, 2010.
 Diagana, Toka; Existence of Weighted PseudoAlmost Periodic Solutions to Some Classes of Nonautonomous Partial Evolution Equations. Nonlinear Analysis (in press). September, 2010.
 Diagana, Toka (with G. M. Mophou and G. M. N'Guérékata) On the existence of mild solutions to some semilinear fractional integrodifferential equations. E. J. Qualitative Theory of Diff. Equ., No. 58. (2010), pp. 117.
 Diagana, Toka (with Attimu Dodzi) Representation of Bilinear Forms by Linear Operators In NonArchimedean Hilbert Space Equipped with a Krull Valuation. Rendiconti Seminario Matematico Università e Politecnico di Torino. Vol. 68 (2010), no. 2, pp. 139159.
 Diagana, Toka (with P. H. Bezandry) Existence of squaremean almost periodic mild solutions to some nonautonomous stochastic secondorder differential equations, Electronic Journal of Differential Equations. Vol. 2010(2010), No. 124, pp. 125.
 Diagana, Toka; Existence of Almost Automorphic Solutions to Some Classes of Nonautonomous HigherOrder Differential Equations. Electronic Journal of Qualitative Theory of Differential Equations, No. 22 (2010), pp. 126.
 Diagana, Toka (with Paul H. Bezandry) Existence of SquareMean Almost Periodic Solutions to Some Stochastic Hyperbolic Differential Equations with Infinite Delay. Commun. Math. Anal. 8 (2010), no. 2, pp. 103124. (Special Issue in Honor of Prof. Peter D. Lax.)
 Diagana, Toka; Existence of Pseudo Almost Automorphic Solutions to a Nonautonomuous Heat Equation. Cubo: A Mathematical Journal. (2009). (in press).
 Diagana, Toka; PseudoAlmost Automorphic Solutions to Some Classes of Nonautonomous Partial Evolution Equations. Differential Equations and Applications 1 (2009), no. 4, pp. 561–582.
 Diagana, Toka (with Paul H. Bezandry) Existence of square quadraticmean almost periodic solutions to some stochastic hyperbolic differential equations. Electron. J. Differential Equations Vol. 2009(2009), No. 111, pp. 114.
 Diagana, Toka; Pseudo Almost Automorphic Solutions to Some Neutral Delay Integral Equations of Advanced Type. Afr. Diaspora J. Math. 8(2009), No. 2, pp. 9099. (Special Issue in Memory of Prof. Ibni Oumar Mahamat Saleh.)
 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 S^{p}Weighted Pseudo Almost Periodic Coefficients. Nonlinear Analysis (2009). (in press).
 Diagana, Toka (with Ravi Agarwal) Existence of Pseudo Almost Automorphic Solutions for the Heat Equation with S^{p}Pseudo Almost Automorphic Coefficients. Boundary Value Problems (2009). (in press).
 Diagana, Toka (with George D. McNeal); Erratum to: "Spectral Analysis for Rank One Perturbations of Diagonal Operators in NonArchimedean Hilbert Space".Commentationes Mathematicae Univ. Carolin. (2009). (in press).
 Diagana, Toka (with George D. McNeal); Spectral Analysis for Rank One Perturbations of Diagonal Operators in NonArchimedean Hilbert Space. Commentationes Mathematicae Univ. Carolin. 50(2009), no. 3, pp. 385400.
 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. 2526.
 Diagana, Toka; Existence of Solutions to Some Classes of Partial Fractional Differential Equations. Nonlinear Analysis. (2009). (in press).
 Diagana, Toka (with Dodzi Attimu); Functional Calculus for a Class of Unbounded Linear Operators on Some NonArchimedean Banach Spaces. Commentationes Mathematicae Univ. Carolin. 50(2009), no. 1, 3760.
 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 1828.
 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 7484.
 Diagana, Toka (with E. Hernandez and J. P. C. dos Santos); Existence of Asymptotically Almost Automorphic Solutions to Some Abstract Partial Neutral IntegroDifferential Equations. Nonlinear Analysis (2008). (in press).
 Diagana, Toka (with P. H. Bezandry); Existence of S^{2}Almost Periodic Solutions to a Class of Nonautonomous Stochastic Evolution Equations. E. J. Qualitative Theory of Diff. Equ., No. 35. (2008), pp. 119.
 Diagana, Toka; On the Existence of Almost Automorphic Solutions to Some Abstract Hyperbolic Differential Equations. Bulletin of the Belgian Mathematical Society (2008). (in press).
 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. 114.
 Diagana, Toka; Existence of Almost Automorphic Solutions to Some Partial Hyperbolic Differential Equations with S^{p}Almost Automorphic Coefficients. Proceedings of the 6^{th} International Conference on Differential Equations and Dynamical Systems held at Morgan State University, Maryland, May 2226, 2008. Dynamics of Continuous, Discrete and Impulsive Systems, Series A (2008). (in press).
 Diagana, Toka; Existence of Pseudo Almost Automorphic Solutions to Some Abstract Differential Equations with S^{p}Pseudo Almost Automorphic Coefficients. Nonlinear Anal (2008). (in press)
 Diagana, Toka; Weighted Pseudo Almost Periodic Solutions to Some Neutral Delay Integral Equation of Advanced Type. Nonlinear Anal. 70 (2009), Issue 1, Pages 298304.
 Diagana, Toka; Stepanovlike Pseudo Almost Periodicity and Its Applications to Some Nonautonmous Differential Equations. Nonlinear Anal. 69 (2009), Issue 12, Pages 42774285.
 Diagana, Toka; Henriquez, Hernan R.; and Hernandez M., Eduardo; Asymptotically Almost Periodic Solutions to Some Classes of SecondOrder Functional Differential Equations. Differential and Integral Equations 21 (2008), nos. 56, 575600.
 Diagana, Toka; Henriquez, Hernan R.; and Hernandez M., Eduardo, Almost Automorphic Solutions to Some Partial Neutral Functional Differential Equations. Nonlinear Anal. 69 (2008), 14851493.
 Diagana, Toka; Existence of weighted pseudo almost periodic solutions to some nonautonomous differential equations. Int. J. Evol. Equ. 2 (2008), no. 4, 397410. (MR2403848)
 Diagana, Toka; Weighted pseudoalmost periodic solutions to some differential equations. Nonlinear Anal. 68 (2008), no. 8, 22502260. (MR2398647)
 Bezandry, Paul H.; Diagana, Toka; Elaydi, Saber; On the stochastic BevertonHolt equation with survival rates. J. Difference Equ. Appl. 14 (2008), no. 2, 175190. (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:"FixedPoint and Ergodic Theorems for Nonexpansive Mappings on Ultrametric Banach Spaces"
 Dodzi Attimu, Howard University, Department of Mathematics, February 2008
Thesis: "Linear Operators on Some NonArchimedean Hilbert Spaces and Their Spectral Theory"
 Najja AlIslam, Howard University, Department of Mathematics, January 2009
Thesis: "Pseudo Almost Periodic Solutions to Some Systems of Nonlinear Hyperbolic SecondOrder Partial Differential Equations"
 George D. McNeal, Howard University, Department of Mathematics, November 2009
Thesis: "Spectral Analysis for RankOne Perturbations of Diagonal Operators in NonArchimedean Hilbert Space"
PROFESSIONAL COMMITTEES/PANELS

IBNI OUMAR MAHAMAT SALEH Prize Panel (2009present)

The American Mathematical Society "COMMITTEE ON HUMAN RIGHTS OF MATHEMATICIANS" (20112014)

The Amercian Mathematical Society "BOOKS AND JOURNAL DONATIONS STEERING COMMITTEE" (20102013)
EDITORSHIP
LINKS
NONMATHEMATICAL ARTICLES

