Publications

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Articles in Review

  1. H. Antil, U. Biccari, R. Ponce, M. Warma, and S. Zamorano
    Controllability properties from the exterior under positivity constraints for a 1--D fractional heat equation.
    Submitted. arxiv

  2. H. Antil, C. Lizama, R. Ponce, and M. Warma
    Convergence of solutions of discrete semi-linear space-time fractional evolution equations.
    Submitted. arxiv

Book

  1. C. G. Gal and M. Warma.
    Fractional-in-Time Semilinear Parabolic Equations and Applications.
    Springer 2020. Link

Published Articles

  1. G. Leugering, G. Mophou, M. Moutamal, and M. Warma.
    Optimal control problems of parabolic fractional Sturm-Liouville equations in a star graph.
    Mathematical Control and Related Field, to appear. arxiv

  2. C. Lizama, M. Warma, and S. Zamorano.
    Exterior controllability properties of a nonlocal Moore-Gibson-Thompson equation.
    Fractional Calculus and Applied Analysis, to appear.

  3. H. Antil, C.G. Gal, and M. Warma.
    A unified framework for optimal control of fractional in time subdiffusive semilinear PDEs
    Discrete and Continuous Dynamical Systems, to appear.

  4. H. Antil, T.S. Brown, D. Verma, and M. Warma.
    Optimal Control of Fractional PDEs with State and Control Constraints.
    Pure and Applied Functional Analysis, to appear.

  5. J-D. Gjida, G. Mophou and M. Warma.
    Optimal Control of mixed local-nonlocal parabolic PDE with singular boundary-exterior data.
    Evolution Equations and Control Theory, to appear. arxiv

  6. U. Biccari, M. Warma, and E. Zuazua
    Control and numerical approximation of fractional diffusion equations.
    Handbook of Numerical Analysis 23 (2022), 1--58. ScienceDirect

  7. H. Antil, T. Brown, R. Khatri, A. Onwunta, D. Verma, and M. Warma
    Optimal control,numerics, and applications of fractional PDEs.
    Handbook of Numerical Analysis 23 (2022), 87--114. ScienceDirect

  8. E. Aragones, V. Keyantuo, and M. Warma
    Approximate and mean approximate controllability properties for Hilfer time-fractional differential equations.
    Vietnam Journal of Mathematics 49 (2021), 739--765. Springer

  9. C. Louis-Rose and M. Warma
    Approximate controllability from the exterior of space time fractional wave equations.
    Applied Mathematics and Optimization 83 (2021), 207--250. Springer

  10. R. Ponce and M. Warma
    Asymptotic behavior and representation of solutions to a Volterra kind of equation with a singular kernel.
    Semigroup Forum 102 (2021), 250--273. Springer

  11. M. Warma and S. Zamorano.
    Exponential Turnpike property for fractional parabolic equations with non-zero exterior data.
    ESAIM Control Optim. Calc. Var. 27 (2021), Paper No. 1, 35 pp. Springer

  12. B. Claus and M. Warma.
    Realization of the fractional Laplacian with nonlocal exterior conditions via forms method.
    J. Evolution Equations 20 (2020), 1597--1631. Springer

  13. M. Warma and S. Zamorano
    Analysis of the controllability from the exterior of strong damping nonlocal wave equations.
    ESAIM Control Optim. Calc. Var. 26 (2020), Paper No. 42, 34 pp. ESIAM

  14. U. Biccari, M. Warma, and E. Zuazua
    Controllability of the one-dimensional fractional heat equation under positivity constraints.
    Communications on Pure and Applied Analysis 19 (2020), 1949--1978. AIMS

  15. V. Keyantuo, L. Tebou, and M. Warma
    A Gevrey class semigroup for a Thermoelastic plate model with a fractional Laplacian: Between the Euler-Bernoulli and Kirchhoff models.
    Discrete and Continuous Dynamical Systems (DCDS) Series A 40 (2020), 2875--2889. AIMS

  16. U. Biccari and M. Warma
    Null-controllability properties of a fractional wave equation with a memory term.
    Evolution Equations and Control Theory 9 (2020), 399--430. AIMS

  17. H. Antil, D. Verma, and M. Warma
    Optimal Control of Fractional Elliptic PDEs with State Constraints and Characterization of the dual of Fractional Order Sobolev Spaces.
    Journal of Optimization Theory and Applications (JOTA) 2020. arxiv

  18. H. Antil, D. Verma, and M. Warma.
    External optimal control of fractional parabolic PDEs.
    ESAIM: Control, Optimisation and Calculus of Variations (CoCV), Volume: 26, Article Number: 20, Pages: 33, Year: 2020. arxiv

  19. H. Antil and M. Warma.
    Optimal control of fractional semilinear PDEs.
    ESAIM: Control, Optimisation and Calculus of Variations (ESAIM: COCV), Volume: 26, Article Number : 5, Pages: 30. 2020. arxiv

  20. H. Antil, R. Khatri, and M. Warma.
    External optimal control of nonlocal PDEs.
    Inverse Problems 35(8) 2019. arxiv

  21. H. Antil and M. Warma.
    Optimal control of the coefficient for regional fractional p-Laplace equation: Approximation and convergence.
    Mathematical Control & Related Fields, 9(1), pp 1-38, 2019. arxiv

  22. M. Warma and S. Zamorano.
    Null controllability from the exterior of a one-dimensional nonlocal heat equation.
    Control & Cybernetics 48 (2019), 417--438. CC

  23. V. Keyantuo, F. Seoanes, and M. Warma.
    Fractional Gaussian estimates and holomorphy of semigroups.
    Archiv der Mathematik 113 (2019), 629--647. Springer

  24. M. Warma.
    Approximate controllability from the exterior of space-time fractional diffusive equations.
    SIAM Journal on Control and Optimization (SICON) 57 (2019), 2037--2063. SIAM

  25. V. Keyantuo, C. Lizama, and M. Warma.
    Lattice dynamical systems associated to a fractional Laplacian.
    Numerical Functional Analysis and Optimization 40 (2019), 1315–-1343. Taylor & Francis Online

  26. Gonzalez-Camus, V. Keyantuo, C. Lizama, and M. Warma.
    Fundamental solutions for discrete dynamical systems involving the fractional Laplacian..
    Mathematical Methods in the Applied Sciences (MMAS) 42 (2019), 4688--4711. MMAS

  27. E. Alvarez, C. G. Gal, V. Keyantuo, and M. Warma.
    Well-posedness results for a class of semi-linear super-diffusive equations.
    Nonlinear Analysis 1181 (2019), 24--61. ScienceDirect

  28. V. Keyantuo, C. Lizama, S. Rueda, and M. Warma.
    Asymptotic behavior of mild solutions for a class of abstract nonlinear difference equations of convolution type.
    Advances in Difference equations (2019), 2019:251. Springer

  29. R. Chill and M. Warma.
    Corrigendum to: Dirichlet and Neumann boundary conditions for the p-Laplace operator: What is in between?
    Proc. Roy. Soc. Edinburgh Sect. A 149 (2019), 1689–1691. cambrigde.org

  30. H. Antil and M. Warma.
    Optimal control of the coefficient for fractional p-Laplace equation: Approximation and convergence.
    RIMS Kokyuroku, 2090, 102--116, 2018.

  31. U. Biccari, M. Warma, and E. Zuazua.
    Local regularity for fractional heat equations.
    Recent Advances in PDEs: Analysis, Numerics and Control. SEMA-SIMAI Springer Series (2018), 223--249. Springer

  32. M. Warma.
    On the (s, p)-Dirichlet-to-Neumann operator on bounded Lipschitz domains.
    Journal of Elliptic and Parabolic Equations (2018), 223--269. Springer

  33. W. Arendt, A. F.M. ter Elst, and M. Warma.
    Fractional powers of sectorial operators via the Dirichlet-to-Neumann operator.
    Communication in Partial Differential Equations 43 (2018), no. 1, 1--24. Taylor & Francis Online

  34. H. Antil, J. Pfefferer, and M. Warma.
    A note on semilinear fractional elliptic equation: analysis and discretization.
    Math. Model. Numer. Anal. (ESAIM: M2AN) 51 (6) (2017). arxiv

  35. V. Keyantuo, C. Lizama, and M. Warma.
    Existence, regularity and representation of solutions of fractional wave equations.
    Electronic Journal of Differential Equations 2017 (2017), No. 222, pp. 1-42. EJDE

  36. M. Warma.
    On the approximate controllability from the boundary for fractional wave equations.
    Applicable Analysis 96 (2017), 2291--2315. Taylor & Francis Online

  37. C. G. Gal and M. Warma.
    Nonlocal transmission problems with fractional diffusion and boundary conditions on non-smooth interfaces.
    Communication in Partial Differential Equations 42 (2017), 579--625. Taylor & Francis Online

  38. C. G. Gal and M. Warma.
    On some degenerate non-local parabolic equations associated with the fractional p-Laplacian.
    Dynamics of PDE 14 (2017), 47--77. International Press

  39. C. G. Gal and M. Warma.
    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. hindawi

  40. U. Biccari, M. Warma, and E. Zuazua.
    Addendum: Local elliptic regularity for the Dirichlet fractional Laplacian.
    Advanced Nonlinear Stud. 17 (2017), 837--839. De Gruyter

  41. U. Biccari, M. Warma, and E. Zuazua.
    Local elliptic regularity for the Dirichlet fractional Laplacian.
    Advanced Nonlinear Studies 17 (2017), 387--409. De Gruyter

  42. C. G. Gal and M. Warma.
    Bounded solutions for nonlocal boundary valued problems on Lipschitz manifolds with boundary.
    Advanced Nonlinear Studies 16 (2016), 529--550. De Gruyter

  43. C. G. Gal and M. Warma.
    Elliptic and parabolic equations with fractional diffusion and dynamic boundary conditions.
    Evolution Equations and Control Theory 5 (2016), 61--103. AIMS

  44. V. Keyantuo, C. Lizama, and M. Warma.
    Existence, regularity and representation of solutions of time fractional diffusion equations.
    Advances in Differential Equations 21 (9/10) (2016), 837--886. euclid

  45. V. Keyantuo and M. Warma.
    On the interior approximate controllability for fractional wave equations.
    Discrete Contin. Dyn. Syst. Ser. A 36 (2016), 3719--3739. AIMS

  46. M. Warma.
    Local Lipschitz continuity of the inverse of the fractional p-Laplacian. Holder type continuity and continuous dependence of solutions to associated parabolic equations on bounded domains.
    Nonlinear Analysis 135 (2016), 129--157. Elsevier

  47. M. Warma.
    The fractional Neumann and Robin boundary condition for the fractional p-Laplacian on open sets.
    NoDEA Nonlinear Differential Equations Appl. 23 (2016), 1--46. Springer

  48. C. G. Gal and M. Warma.
    Transmission problems with nonlocal Wentzell type boundary conditions and rough dynamic interfaces.
    Nonlinearity 29 (2016), 161--197. IOPScience

  49. C. G. Gal and M. Warma.
    Reaction-diffusion equations with fractional diffusion on non-smooth domains with various boundary conditions.
    Discrete Contin. Dyn. Syst. Ser. A 36 (2016) 1279--1319. AIMS

  50. M. Warma.
    A fractional Dirichlet-to-Neumann operator.
    Commun. Pure Appl. Anal. 14 (2015), 2043--2067. AIMS

  51. M. Warma.
    The fractional relative capacity and the fractional Laplacian with Neumann and Robin boundary conditions on open sets.
    Potential Analysis 42 (2015) , 499--547. Springer

  52. M. Warma.
    The p-Laplace operator with the nonlocal Robin boundary conditions on arbitrary open sets.
    Ann. Mat. Pura Appl. 193 (2014), 203--235. Springer

  53. P. Sacks and M. Warma.
    Semi-linear elliptic and elliptic-parabolic equations with Wentzell boundary conditions and L^1-data.
    Discrete Contin. Dyn. Syst. Ser. A 34 (2014), 763--789. AIMS

  54. V. Keyantuo, C. Lizama, and M. Warma.
    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. Hindawi

  55. V. Keyantuo, C. Lizama, and M. Warma.
    Asymptotic behavior of fractional order semilinear evolution equations.
    Differential Integral Equations 26 (2013), 757--780. euclid

  56. M. Warma.
    Semi linear parabolic equations with nonlinear general Wentzell boundary conditions.
    Discrete Contin. Dyn. Syst. Ser. A 33 (2013), 5493--5506. AIMS

  57. C. G. Gal and M. Warma.
    Existence of bounded solutions for a class of quasilinear elliptic systems on manifolds with boundary.
    J. Differential Equations 255 (2013), 151--192. ScienceDirect

  58. R. Chill and M. Warma.
    A Riesz type representation for lower semicontinuous, monotone, local functionals on C_c (X)^+.
    Nonlinear Analysis 85 (2013), 17--22. ScienceDirect

  59. M. Warma.
    Parabolic and elliptic problems with general Wentzell boundary conditions on Lipschitz domains.
    Commun. Pure Appl. Anal. 12 (2013), 1881--1905. AIMSt

  60. R. Chill and M. Warma.
    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. Cambridge

  61. M. Warma.
    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. Elsevier

  62. E. Avarez-Pardo and M. Warma.
    The one-dimensional wave equation with general boundary conditions.
    Archiv der Mathematik (Basel) 96 (2011), 177--186. Springer

  63. M. Biegert and M. Warma.
    Existence of solutions to some quasi-linear PDEs with generalized Robin boundary conditions.
    Nonlinear Analysis 73 (2010), 1853--1863. ScienceDirect

  64. M. Warma.
    Analyticity on L_1 of the heat semigroup with Wentzell boundary conditions.
    Archiv der Mathematik (Basel) 94 (2010), 85--89. Springer

  65. M. Biegert and M. Warma.
    Some quasi-linear elliptic equations with inhomogeneous generalized Robin boundary conditions on ``bad'' domains.
    Advances in Differential Equations 15 (2010), 893--924. euclid

  66. A. Velez-Santiago and M. Warma.
    A class of quasi-linear parabolic and elliptic equations with nonlocal Robin boundary conditions.
    J. Mathematical Analysis and Applications 372 (2010), 120--139. ScienceDirect

  67. C. G. Gal and M. Warma.
    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. euclid

  68. M. Biegert and M. Warma.
    The heat equation with nonlinear generalized Robin boundary conditions.
    J. Differential Equations 247 (2009), 1949--1979. ScienceDirect

  69. M. Warma.
    An ultracontractivity property for semigroups generated by the p-Lapalcian with nonlinear Wentzell-Robin boundary conditions.
    Advances in Differential Equations 14 (2009), 771--800. euclide

  70. R. Chill and M. Warma.
    Generation of cosine families on L^p (0,1) by elliptic operators with Robin boundary conditions.
    Birkhauser. Functional Analysis and Evolution Equations. 2008, 113--130. Springer

  71. M. Warma.
    Quasilinear parabolic equations with nonlinear Wentzell-Robin type boundary conditions.
    J. Mathematical Analysis and Applications 336 (2007), 1132--1148. ScienceDirect

  72. M. Warma.
    The Robin and Wentzell-Robin Laplacians on Lipschitz domains.
    Semigroup Forum 73 (2006), 10--30. Springer

  73. M. Biegert and M. Warma.
    Regularity in capacity and the Dirichlet Laplacian.
    Potential Analysis 25 (2006), 289--305. Springer

  74. V. Keyantuo and M. Warma.
    The wave equation with Wentzell-Robin boundary conditions on L^p-spaces.
    J. Differential Equations 229 (2006), 680--697. ScienceDirect

  75. M. Biegert and M. Warma.
    Removable singularities for a Sobolev space.
    J. Mathematical Analysis and Applications 313 (2006), 49--63. ScienceDirect

  76. V. Keyantuo and M. Warma.
    The wave equation in L^p-spaces..
    Semigroup Forum 71 (2005), 73--92. Springer

  77. W. Arendt and M. Warma.
    The Laplacian with Robin boundary conditions on arbitrary domains.
    Potential Analysis 19 (2003), 341--363. Springer

  78. W. Arendt and M. Warma.
    Dirichlet and Neumann boundary conditions: What is in between?
    J. Evolution Equations 3 (2003), 119--135. Springer

  79. M. Warma.
    Wentzell-Robin boundary conditions on C[0,1].
    Semigroup Forum 66 (2003), 162--170. Springer