Publications

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Articles in Review

  1. H. Antil, T.S. Brown, D. Verma and M. Warma.
    Optimal Control of Fractional PDEs with State and Control Constraints.
    Submitted 2021.

  2. 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 2019. arxiv

  3. H. Antil, C. Lizama, R. Ponce, and M. Warma
    Convergence of solutions of discrete semi-linear space-time fractional evolution equations.
    Submitted 2019. arxiv

Book

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

Published Articles

  1. C. Louis-Rose and M. Warma
    Approximate controllability from the exterior of space time fractional wave equations.
    Accepted in Applied Mathematics and Optimization. Springer

  2. E. Aragones, V. Keyantuo, and M. Warma
    Approximate and mean approximate controllability properties for Hilfer time-fractional differential equations.
    Accepted in Vietnam Journal of Mathematics 2021. Springer

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

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

  14. 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

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

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

  17. 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

  18. 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

  19. 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

  20. 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

  21. 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

  22. 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

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

  24. 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

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

  26. 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

  27. 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

  28. 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

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

  30. 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

  31. 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

  32. 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

  33. 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

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

  35. 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

  36. 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

  37. 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

  38. 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

  39. 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

  40. 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

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

  42. 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

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

  44. 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

  45. 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

  46. 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

  47. 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

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

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

  50. 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

  51. 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

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

  53. 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

  54. 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

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

  56. 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

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

  58. 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

  59. 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

  60. 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

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

  62. 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

  63. 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

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

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

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

  67. 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

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

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

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

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

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