Professor Information

Mahamadi Warma

Address College of Natural Sciences
Department of Mathematics
17 University Ave. Ste 1701
San Juan, PR 00925-2537
Office NCN II C-112
Office Hours
Program
Telephone (787) 764-0000 88258
E-Mail moc.liamg@amrawjm, ude.rpu@1amraw.idamaham
MathSciNet Link

Education

PhD, University of Ulm (Germany), 2002

Research

Linear and nonlinear Potential Theory; Linear and nonlinear Partial Differential Equations; Functional Analysis; Evolution Equations; Semigroups of Operators

Selected Publications

  1. (with H. Antil) Optimal control of the coefficient for fractional and regional fractional p-Laplace equations: Approximation and convergence. Mathematical Control and Related Fields, to appear.
  2. (with U. Biccari and E. Zuazua) Local regularity for fractional heat equations. SEMA- SIMAI Springer Series, to appear.
  3. Mahamadi Warma. On a fractional (s, p)-Dirichlet-to-Neumann operator on bounded Lipschitz domains. Journal of Elliptic and Parabolic Equation 4 (2018), 223–269.
  4. Mahamadi Warma (with W.Arendt and A.F.M. Ter Elst) Fractional powers of sectorial operators via the Dirichlet-to-Neumann operator. Comm. Partial Differential Equations 43 (2018), no. 1, 1–24.
  5. (with V. Keyantuo and C. Lizama) Existence, regularity and representation of solutions of fractional wave equations. Electronic Journal of Differential Equations 2017 (2017), No. 222, pp. 1-42.
  6. On the approximate controllability from the boundary for fractional wave equations. Applicable Analysis 96 (2017), 2291–2315.
  7. (with H. Antil and J. Pfefferer) A note on semilinear fractional diffusion equation: analysis and discretization. Mathematical Modelling and Numerical Analysis. ESAIM: M2AN 51 (2017), 2049–2067.
  8. (with C. G. Gal). Nonlinear elliptic boundary value problems at resonance with nonlinear Wentzell-Robin type boundary conditions. Advances in Mathematical Physics 2017 (2017), Article ID 5196513, 20 pages.
  9. (with U. Biccari and E. Zuazua) Addendum: Local elliptic regularity for the Dirichlet fractional Laplacian. Adv. Nonlinear Stud. 17 (2017), 837–839.
  10. (with U. Biccari and E. Zuazua) Local elliptic regularity for the Dirichlet fractional Laplacian. Advanced Nonlinear Studies 17 (2017), 387–409.
  11. (with C. G. Gal) Nonlocal transmission problems with fractional diffusion and bound- ary conditions on non-smooth interfaces. Communication in Partial Differential Equations 42 (2017), 579–625.
  12. (with C. G. Gal) On some degenerate non-local parabolic equations associated with the fractional p-Laplacian. Dynamics of PDE 14 (2017), 47–77.
  13. (with C.G. Gal). Long-term behavior of reaction-diffusion equations with nonlocal boundary conditions on nonsmooth domains. Zeitschrift fu ̈r angewandte Mathematik und Physik ZAMP 67 (2016), no. 4, Art. 83, 42 pp.
  14. (with C. G. Gal) Bounded solutions for nonlocal boundary valued problems on Lipschitz manifolds with boundary. Advanced Nonlinear Studies 16 (2016), 529–550.
  15. (with V. Keyantuo and C. Lizama). Existence, regularity and representation of solu- tions of time fractional diffusion equations. Advances in Differential Equations 21 (9/10) (2016), 837–886.
  16. (with C. G. Gal) Elliptic and parabolic equations with fractional diffusion and dynamic boundary conditions. Evolution Equations and Control Theory 5 (2016), 61– 103.
  17. (with V. Keyantuo) On the interior approximate controllability for fractional wave equa tions. Discrete Contin. Dyn. Syst. Ser. A 36 (2016), 3719–3739.
  18. Local Lipschitz continuity of the inverse of the fractional p-Laplacian, Ho ̈lder type continuity and continuous dependence of solutions to associated parabolic equations on bounded domains. Nonlinear Analysis 135 (2016), 129–157.
  19. The fractional Neumann and Robin boundary condition for the fractional p-Laplacian on open sets. NoDEA Nonlinear Differential Equations Appl. 23 (2016), 1–46.
  20. (with C. G. Gal) Transmission problems with nonlocal Wentzell type boundary conditions and rough dynamic interfaces. Nonlinearity 29 (2016), 161–197.
  21. (wth C. G. Gal) Reaction-diffusion equations with fractional diffusion on non-smooth domains with various boundary conditions. Discrete Contin. Dyn. Syst. Ser. A 36 (2016) 1279–1319.
  22. A fractional Dirichlet-to-Neumann operator. Commun. Pure Appl. Anal. 14 (2015), 2043–2067.
  23. The fractional relative capacity and the fractional Laplacian with Neumann and Robin boundary conditions on open sets. Potential Analysis 42 (2015) , 499–547.
  24. The p-Laplace operator with the nonlocal Robin boundary conditions on arbitrary open sets. Ann. Mat. Pura Appl. 193 (2014), 203–235.
  25. (with P. Sacks) Semi-linear elliptic and elliptic-parabolic equations with Wentzell boundary conditions and L1-data. Discrete Contin. Dyn. Syst. Ser. A 34 (2014), 763–789.
  26. (with V. Keyantuo and C. Lizama). Spectral criteria for solvability of boundary value problems and positivity of solutions of time-fractional differential equations. Abstract Applied Analysis (2013), Article ID 614328, 11 pages.
  27. (with V. Keyantuo and C. Lizama) Asymptotic behavior of fractional order semilinear evolution equations. Differential Integral Equations 26 (2013), 757–780.
  28. Semi linear parabolic equations with nonlinear general Wentzell boundary conditions. Discrete Contin. Dyn. Syst. Ser. A 33 (2013), 5493–5506.
  29. (with Ciprian G. Gal) Existence of bounded solutions for a class of quasilinear elliptic systems on manifolds with boundary. J. Differential Equations 255 (2013), 151– 192.
  30. (with R. Chill) A Riesz type representation for lower semicontinuous, monotone, local functionals on Cc(X)+. Nonlinear Analysis 85 (2013), 17–22.
  31. Parabolic and elliptic problems with general Wentzell boundary conditions on Lipschitz domains. Commun. Pure Appl. Anal. 12 (2013), 1881–1905.
  32. (with R. Chill) Dirichlet and Neumann boundary conditions for the p-Laplace operator: What is in between? Proceedings of the Royal Society of Edinburgh, Section A 142 (2012), 975–1002.
  33. Regularity and well-posedness of some quasi-linear elliptic and parabolic problems with nonlinear general Wentzell boundary conditions on nonsmooth domains. Nonlinear Analysis 75 (2012) 5561–5588.
  34. (with E. Alvarez-Pardo). The one-dimensional wave equation with nonlocal Robin boundary conditions. Archiv der Mathematik (Basel) 96 (2011), 177–186.
  35. Analyticity on L1 of the heat semigroup with Wentzell boundary conditions. Archiv der Mathematik (Basel) 94 (2010), 85-89.
  36. (with M. Biegert). Existence of solutions to some quasi-linear PDEs with generalized Robin boundary conditions. Nonlinear Analysis 73 (2010), 1853-1863.
  37. (with M. Biegert). Some quasi-linear elliptic equations with inhomogeneous generalized Robin boundary conditions on “bad” domains. Advances in Differential Equations 15 (2010), 893-924.
  38. (with A. Velez-Santiago). A class of quasi-linear parabolic and elliptic equations with nonlocal Robin boundary conditions. J. Mathematical Analysis and Applications 372 (2010), 120-139.
  39. (with C. G. Gal). Well-posedness and the global attractor of some quasi-linear parabolic equations with nonlinear dynamic boundary conditions. Differential and Integral Equations 23 (2010), 327–358.
  40. (with M. Biegert). The heat equation with nonlinear generalized Robin boundary conditions. J. Differential Equations 247 (2009), 1949–1979.
  41. An ultracontractivity property for semigroups generated by the p-Lapalcian with non- linear Wentzell-Robin boundary conditions. Advances in Differential Equations 14 (2009), 771–800.
  42. (with R. Chill and V. Keyantuo). Generation of cosine families on Lp(0,1) by elliptic operators with Robin boundary conditions. Birkhau ̈ser. Functional Analysis and Evolution Equations. 2008, 113–130.
  43. Quasilinear parabolic equations with nonlinear Wentzell-Robin type boundary conditions. J. Math. Anal. Appl. 336 (2007), 1132-1148.
  44. with V. Keyantuo) The wave equation with Wentzell-Robin boundary conditions on Lp -spaces. J. Differential Equations, 229 (2006), 680-697.
  45. (with M. Biegert) Regularity in capacity and the Dirichlet Laplacian. Potential Anal. 25 (2006), 289-305.
  46. (with W. Arendt) Dirichlet and Neumann boundary conditions: What is in between? J. Evol. Equ. 3 (2003), 119-135.
  47. Wentzell-Robin boundary conditions on C [0, 1]. Semigroup Forum 66 (2003), 162-170.

Selected Grants and Awards

  1. AFOSR Grant FA9550-18-1-0242. (PI) Nonlocal PDEs: Analysis, Control and Beyond. June 2018–May 2021 (Total: $456,494).
  2. AFOSR Grant FA9550-15-1-0027. (PI) Dynamics, Control and Numerics for Fractional Partial Differential Equations. December 2014–May 2018 (Total: $450,438)
  3. ARO Grant W911NF-17-1-0286. (PI) Workshop on Dynamics, Control and Numerics for Fractional PDEs. May 2017– December 31, 2018. (Total: $18,600.00)
  4. AFOSR Grant FA9550-17-1-0524. (PI) Workshop on Dynamics, Control and Numerics for Fractional PDEs. September 30, 2017 — March 31, 2019. (Total: $39, 853.00)

Additional Information