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Pablo Álvarez Caudevilla

Titular de Universidad
(Associate Professor)

Office: 2.2A05(Edificio Sabatini)
Phone: +34 916249099
E-Mail: This email address is being protected from spambots. You need JavaScript enabled to view it.


Curriculum Vitae: spanish/english

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List of Publications

  1. On a class of linear cooperative systems with spatio-temporal degenerate potentials, Mediterranean Journal of Mathematics, (2021) in press (with Fernando Belinchón and Cristina Brändle)

  2. Asymptotic limit of linear parabolic equations with spatio-temporal degenerated potentials, ESAIM Control Optim. Cal. Var. 26 (2020), Paper No. 50, 20 pp (with Matthieu Bonnivard and Antoine Lemenant)

  3. Positive solutions for semilinear fractional elliptic problems involving an inverse fractional operator. Nonlinear Anal. Real World App., 51, (2020) (with Eduardo Colorado and Alejandro Ortega)

  4. Homotopy regularization for a high--order parabolic equation}. Mediterr. J. Math. 17, 2 (2020) (with Alejandro Ortega)

  5. Gradient Blow-up for a fourth-order quasilinear Boussinesq.type equation, Discrete and Continuous Dynamical Systems-A, 38 Number 8 (2018) 3913--3938 (with Jonathan D. Evans and Victor Galaktionov)

  6. On the existence of coexistence states for an advection-cooperative system with spatial heterogeneities, Nonlinear Analysis. 152 (2017) 12--37 (with Tatsuya Watanabe)

  7. A higher order system of some coupled nonlinear Schrödinger and Korteweg-de Vries equations}. J. Math. Phys. 58 (2017), no. 11 (with Eduardo Colorado and Rasiel Fabelo)

  8. Existence and multiplicity of stationary solutions for a Cahn--Hilliard-type equation in RN, Discrete Contin. Dyn. Syst. AIMS Proceedings (2015) 10-18

  9. Blow-up scaling and global behaviour of solutions of the bi-Laplace equation via pencil operators}, Comm. Pure and Appl. Anal., 15 (2016) no. 1, 261--286 (with Victor A. Galaktionov)

  10. Countable families of solutions of a limit stationary semilinear fourth-order Cahn--Hilliard-type equation I. Mountain pass and Lusternik--Schnirel'man patterns in R^N, Boundary Value Problems, (2016) Paper No. 171, 25 pp
    (with Jonathan D. Evans and Victor Galaktionov)
  11. Existence of solutions for a system of coupled nonlinear stationary bi-harmonic Schrödinger equations, Nonlinear Analysis: Real World Applications, 23, (2015), 78-93 (with Eduardo Colorado and Victor Galaktionov)
  12. On a Branching Analysis of a countable family of global similarity solutions of a fourth-order thin film equation, Electronic Journal of Differential Equations, Vol. 2015 (2015), no. 90, 1-29 (with Victor A.Galaktionov)
  13. Towards optimal regularity for the fourth-order thin film equation in R^N: Graveleau-type focusing self-similarity, Journal of Mathematical Analysis and Applications, 431 (2015), 1099-1123 (with Jonathan D. Evans and Victor A. Galaktionov)
  14. The p-Laplace equation in domains with a multiple crack section via pencil operators, Advances Nonlinear Studies, 15, no. 1 (2015), 91-116  (with Victor A. Galaktionov)
  15. The Cauchy problem for a tenth-order thin film equation II. Oscillatory source-type and fundamental similarity solutions, Discrete Contin. Dyn. Syst., 35, no. 3 (2015), 807-827 (with Jonathan D. Evans and Victor A. Galaktionov)
  16. Well-posedness of the Cauchy problem for a fourth-order thin film equation via regularization approaches, Nonlinear Analysis, 121 (2015), 19-35 (with Victor A.Galaktionov)
  17. Qualitative analysis of a cooperative reaction-diffusion system in spatiotemporally degenerate environment, SIAM Journal of Mathematical Analysis, vol. 46, no. 1 (2014), 499-531 (with Yihong Du and Rui Peng)
  18. The Cauchy problem for tenth-order thin film equation I. Bifurcation of oscillatory fundamental solutions, Mediterranean Journal of Mathematics, No. 4, Vol. 10(2013), 1759-1790  (with Jonathan D. Evans and Victor A. Galaktionov)
  19. Steady states, global existence and blow--up for fourth--order semilinear parabolic equations of Cahn--Hilliard type,  Advances Nonlinear Studies, 12, (2012), 315-361 (with Victor A.Galaktionov)
  20. Variational approach for a class of cooperative systems, Nonlinear Analysis. Theory, Methods and Applications, 75 (2012), 5620-5638
  21. Local bifurcation analysis of global and “blow-up” patterns for a fourth-order thin film equation, Nonlinear Differential equations and Applications (NoDEA), Vol. 18, (2011), 483--537, (with Victor A.Galaktionov)
  22. Asymptotic analysis for some linear eigenvalue problems via Gamma-Convergence, Advances in Differential Equations, Vol. 15, 7-8 (2010), 649-688, (with Antoine Lemenant)
  23. The dynamics of a class of sublinear cooperative systems, Discrete Contin. Dyn. Syst. 26, no. 2, (2010), 397–415, (with Julián López-Gómez)
  24. Characterizing the existence of coexistence states for a class of cooperative systems, Discrete Contin. Dyn. Syst., Supplement (2009), 24–33, with Julián López-Gómez)
  25. Asymptotic behaviour of principal eigenvalues for a class of cooperative systems [Corrigendum J. Differential Equations 245, (2008), no. 2, 566–567], Journal of Differential Equations. 244 (2008), 1093–1113, (with Julián López-Gómez)
  26. Semiclassical Analysis for highly degenerate potentials. Proceedings of American Mathematical Society, 136 (2008), 665–675, (with Julián López-Gómez)
  27. Metasolutions in cooperative systems, Nonlinear Analysis: Real World Applications. 9 (2008), 1119–1157, (with Julián López-Gómez)

 

 

 

 




Teaching

Academic Year 2021-2022.

  • Linear Algebra. First year Bachelor' Degree in Aerospace Engineering (in English).
  • Calculus II. First year Bachelor' Degree in Biomedical Engineering (in English).
  • Ordinary Differential Equations. Third year Bachelor' Degrees in Applied Mathematics and Computing (in English)

Academic Year 2010-2021.

  • Undergraduate Teaching.
  1. Calculus I. First year Bachelor' Degree in Mechanical Engineering (in English).
  2. Calculus II. First year Bachelor' Degrees in Biomedical Engineering (in English) Industrial Technologies and Telematic Engineering.
  3. Calculus III. Third year Bachelor' Degree in Industrial Technologies Engineering (in English).
  4. Linear Algebra. First year Bachelor' Degrees in Aerospace and Industrial Technologies Engineering (in English).
  5. Differential Equations. Second year Bachelor' Degree in Biomedical Engineering (in English).
  6. Advanced Mathematics (Differential Equations). Second year Bachelor' Degree in Aerospace Engineering (in English).
  7. Advanced Mathematics (Complex Variable and ODEs). Second year Bachelor' Degree in Audiovisual Systems Engineering. 
  8. Advanced Mathematics (Linear Algebra). Second year Bachelor' Degree Statistics and Business.
  • Postgraduate Teaching. Partial Differential Equations and Advanced Numerical Methods. Masters in Mathematical Engineering.

 

 
 
 

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