Lineas de Investigación y Artículos

Artículos / Articles:

1. "Eigenvalue Problems for Nonsmoothly Perturbed Domains"
Journal of Differential Equations, Vol 91 (1991) 24-52 (with J. Hale and Q. Han)

2. "A damped hyperbolic equation with critical exponent"
Communications in Partial Differential Equations17 (5 & 6), 841-866 (1992). (with A. Carvalho and J. Hale)

3. "Neumann Eigenvalue Problems on Exterior Perturbations of the Domain"
Journal of Differential Equations, Vol. 118, No. 1, (1995) 54-103

4. "Rates of Eigenvalues on a Dummbell Domain. Simple Eigenvalue Case"
Transactions of the A.M.S. Vol. 347, No. 9, (1995) 3503-3531.

5. "Elliptic Equations, Principal Eigenvalue and Dependence on the Domain"
Communications in Partial Differential Equations, 21 (5\&6), 971-991 (1996)

6. "Domain Dependence of Elliptic Operators in Divergence Form"
Resenhas IME-USP, Vol. 3, No. 1, 107 - 123 (1997).

7. "Critical Nonlinearities at the Boundary"
C.R. Acad. Sci.Paris, t. 327, Série I, p. 353-358, (1998) (with A. Carvalho and A. Rodríguez-Bernal)

8. "Abstract Parabolic Equations with Critical Nonlinearities and Applications to Navier-Stokes and Heat Equations"
Transactions of the A.M.S 352, pp. 285-310 (2000) (with A. Carvalho)

9. "Parabolic Problems with Nonlinear Boundary Conditions and Critical Nonlinearities"
Journal of Differential Equations 156, pp. 376-406 (1999) (with A. Carvalho and A. Rodríguez-Bernal)

10. "Perturbations of the Diffusion and Upper Semicontinuity of Attractors"
Applied Mathematics Letters 12, pp 37-42 (1999) (with A. Carvalho and A. Rodríguez-Bernal)

11. "Attractors of Parabolic Problems with Critical Nonlinearities. Uniform Bounds"
Communications in Partial Differential Equations25, 1&2, pp. 1-37 (2000) (with A. Carvalho and A. Rodríguez-Bernal)

12. "Uppersemicontinuity of Attractors for Parabolic Problems with Localized Large Diffusion and Nonlinear Boundary Conditions"
Journal of Differential Equations 168, pp 33-59 (2000). (with A. Carvalho and A. Rodríguez-Bernal)

13. "Spectral Behavior and Uppersemicontinuity of Attractors"
International Conference on Differential Equations (EQUADIFF'99) Berlin. World Scientific.pp 615-621 (2000).

14. "Parabolic Problems with Dynamical Boundary Condition and Singular Initial Data"
Differential and Integral Equations 14, pp. 1487-1510 (2001) (with P. Quittner and A. Rodríguez-Bernal)

15. "Magnetic Properties of Diruthenium (II,III)Carboxilate Compounds with Large Zero-Field Splitting and Strong Antiferromagnetic Coupling"
Inorganic Chemistry, 40, 613-619, (2001) (with R. Jiménez-Aparicio and F.A. Urbanos)

16. "Pattern Formation from Boundary Reaction"
Fields Inst. Commun., 31, pp. 13-18, Amer. Math. Soc., Providence, RI, (2002). (with N. Consul and A. Rodriguez-Bernal)

17. "Asymptotic Behavior and Attractors for Reaction Diffusion Equations in Unbounded Domains"
Nonlinear Analysis, 56, pp. 515-554 (2004) (with J.W. Cholewa, T. Dlotko and A. Rodríguez-Bernal)

18. "Stable boundary layers in a diffusion problem with nonlinear reaction at the boundary"
Z. angew. Math. Phys. 55, pp. 1-14 (2004) (with N. Consul and A. Rodriguez-Bernal)

19. "Linear parabolic equations in locally uniform spaces"
Mathematical Models and Methods in Applied Sciences, 14, n. 2, 253-294 (2004) (with J.W. Cholewa, T. Dlotko and A. Rodríguez-Bernal)

20. "Boundedness of Global Solutions for Nonlinear Parabolic Equations involving Gradient Blow-up Phenomena"
Annali della Scuola Normale Superiore di Pisa, Classe di Scienze. Issue 1, Volume 3/2004, Series 5, pp 1-15, (2004) (with A. Rodríguez-Bernal and P. Souplet)

21. "Spectral Convergence and Nonlinear Dynamics for Reaction-Diffusion Equations under Perturbations of the Domain"
Journal of Differential Equations 199, pp. 143-178 (2004) (with A. Carvalho)

22. "El Cálculo y la Modelización Matemática", en R. Rodríguez, E. Zuazua,
De la Aritmética al Análisis: Historia y Desarrollo reciente en Matemáticas, Aulas de Verano, Instituto Superior de Formación del Profesorado, Ministerio de Educación y Ciencia,
pp 11-57 (2004)

23. "Localization on the boundary of blow-up for reaction-diffusion equations with nonlinear boundary conditions"
Communications in Partial Differential Equations 29, 7&8, pp. 1127-1148 (2004) (with A. Rodríguez-Bernal)

24. "Non well posedness of parabolic equations with supercritical nonlinearities"
Communications in Contemporary Mathematics 6, n 5, pp. 733-764 (2004) (with A. Rodríguez-Bernal)

25. "Ill posed problems with supercritical nonlinearities''.
International Conference on Differential Equations (EQUADIFF'03) Hasselt, Belgium. World Scientific, pp 277-280, (2005) , (with A. Rodríguez-Bernal)

26. "Nonhomogenous flux condition as limit of localized reactions''.
International Conference on Differential Equations (EQUADIFF'03) Hasselt, Belgium. World Scientific, pp 293-295, (2005), (with A. Jiménez-Casas and A. Rodríguez-Bernal)

27. "Problemas de valor de fronteira em domínios com oscilaçōes na fronteira",
Seminario Brasileiro de Análise, Edición nº 62, Noviembre (2005), (with Simone M. Bruschi)

28. "Boundary Oscillations and Nonlinear Boundary Conditions",
C. R. Acad. Sci. Paris, t. 343, Series I, pp. 99-104 (2006) (with Simone M. Bruschi)

29. "Dynamics in dumbbell domains I. Continuity of the set of equilibria"
Journal of Differential Equations, 231, Issue 2, pp. 551-597, (2006), (with A.N. Carvalho and G. Lozada-Cruz)

30. "Dynamics of a reaction-diffusion equation with a discontinuous nonlinearity",
International Journal of Bifurcation and Chaos 16, n. 10, pp. 2965-2984 (2006) , (with A. Rodríguez-Bernal and J. Valero)

31. "Bifurcation and stability of equilibria with asymptotically linear boundary conditions at infinity",
Proceedings of the Royal Society of Edinburgh A, Vol.137, Issue 02, 225-252. (2007), (with R. Pardo and A. Rodríguez-Bernal)

32. "Rapidly varying boundaries in equations with nonlinear boundary conditions. The case of a Lispschitz deformation"
Mathematical Models and Methods in Applied Sciences, vol 17, No. 10, 1555-1585 (2007) (with Simone M. Bruschi)

33. "Dissipative parabolic equations in locally uniform spaces",
Mathematische Nachrichten 280, Issue 15. pp. 1643-1663, (2007), (with J.W. Cholewa, T. Dlotko and A. Rodríguez-Bernal)

34. “Blow up versus global boundedness of solutions of reaction diffusion equations with nonlinear boundary conditions”,
Proceedings of Equadiff 11, Editors: M.Fila, A.Handlovicova, K.Mikula, M.Medved, P.Quittner and D.Sevcovic (2007). pp 1-7 (with A. Rodríguez-Bernal)

35. “Robin type conditions arising from concentrated potentials”,
Proceedings of Equadiff 11, Editors: M.Fila, A.Handlovicova, K.Mikula, M.Medved, P.Quittner and D.Sevcovic (2007). pp 157-164 (with A. Jiménez-Casas and A. Rodríguez-Bernal)

36. “Dissipative dynamics of reaction diffusion equations in R^N”
Proceedings of Equadiff 11, Editors: M.Fila, A.Handlovicova, K.Mikula, M.Medved, P.Quittner and D.Sevcovic (2007), pp 405-414, (with N. Moya and A. Rodríguez-Bernal)

37. "On boundedness of solutions of reaction-diffusion equations with nonlinear boundary conditions"
Proceedings of the American Mathematical Society 136, Issue 1, pp. 151-160 (2008)

38. "On the finite dimension of attractors of parabolic problems in $R^N$ with general potentials",
Nonlinear Analysis, Theory Methods and Applications 68, Issue 5, pp. 1082-1099 (2008) (with N. Moya and A. Rodríguez-Bernal)

39. "Flux terms and Robin boundary conditions as limit of reactions and potentials concentrating in the boundary"
Revista Matemática Iberoamericana, 24 nº 1, pp. 183- 211 (2008) (with A. Jiménez-Casas and A. Rodríguez-Bernal)

40. "The best Sobolev trace constant as limit of the usual Sobolev constant for small strips near the boundary",
Proceedings of the Royal Society of Edinburgh 138A, 223-237 (2008) (with A. Rodríguez-Bernal and J. Rossi)

41. "Equilibria and global dynamics of a problem with bifurcation from infinity"
Journal of Differential Equations 246, pp. 2055-2080 (2009) (with R. Pardo and A. Rodríguez-Bernal)

42. "Dynamics in dumbbell domains II. The limiting problem" (doi:10.1016/j.jde.2009.03.014 )
Journal of Differential Equations 247, pp 174-202 (2009) (with A. N. Carvalho, G. Lozada-Cruz)

43. "Dynamics in dumbbell domains III. Continuity of attractors"   ( doi:10.1016/j.jde.2008.12.014 )
Journal of Differential Equations, 247, pp. 225-259, (2009) (with A. N. Carvalho, G. Lozada-Cruz)

44. "Geometric vs. spectral convergence for the Neumann Laplacian under exterior perturbations of the domain"
Integral methods in science and engineering.Volume I. Analytic Methods, pp 9-19, Birkhäuser Boston, Boston, MA, (2010) (with David Krejcirik)

45. “Stability of the blow-up time and the blow-up set under perturbations" (doi:10.3934/dcds.2009.26.43)
Discrete and Continuous Dynamical Systems A 26, # 1, pp 43-61 (2010) (with R. Ferreira, A. de Pablo, J.D. Rossi)

46. "Cascades of Hopf bifurcations from boundary delay" (doi:10.1016/j.jmaa.2009.09.018)
Journal of Mathematical Analysis and Applications 361, pp. 19-37 (2010) (with N. Consul and S. Oliva)

47. "Very rapidly varying boundaries in equations with nonlinear boundary conditions. The case of non uniform Lispschitz deformation" (doi:10.3934/dcdsb.2010.14.327)
Discrete and Continuous Dynamical Systems B, Volume 14, Number 2, pp. 327–351 (2010) (with Simone M. Bruschi)

48. "Elliptic problems in thin domains with highly oscillating boundaries",
Bolletin de la Sociedad Española de Matemática Aplicada 51 pp:17-24 (2010) (with M. C. Pereira)

49. "Inﬁnite resonant solutions and turning points in a problem with unbounded bifurcation" (doi: 10.1142/S021812741002743X)
International Journal of Bifurcation and Chaos 20, #9, pp: 2885-2896 (2010) (with   R. Pardo, A. Rodríguez-Bernal)

50. "On the supercriticality of the first Hopf bifurcation in a delay boundary problem" (doi: 10.1142/S0218127410027507)
International Journal of Bifurcation and Chaos 20, #9, pp: 2955-2963 (2010) (with N. Consul and S. Oliva)

51. "Semilinear parabolic problems in thin domains with a highly oscillatory boundary" (doi:10.1016/j.na.2011.05.006)
Nonlinear Analysis: Theory, Methods and Applications 74, #15 pp: 5111-5132 (2011) (with A.N. Carvalho, M.C. Pereira, R.P. da Silva)

52. "Homogenization in a thin domain with an oscillatory boundary"   ( doi:10.1016/j.matpur.2011.02.003)

Journal de Mathématiques Pures et Apliquées 96, #1, pp: 29-57 (2011), (with M.C. Pereira)

53. "On a nonlocal moving frame approximation of traveling waves," (doi:10.1016/j.crma.2011.07.001)
Comptes Rendus Mathematique 349 pp. 753-758 (2011) (with M. López-Fernández, E. Zuazua)

54. "Approximating travelling waves by equilibria of non local equations" (doi: 10.3233/ASY-2011-1088)

un Asymptotic Analysis 78 pp. 145-186 (2012) (with M. López-Fernández, E. Zuazua)

55. "Continuity of dynamical structures for non-autonomous evolution equations under singular perturbations" (doi:10.1007/s10884-012-9269-y)

Journal of Dynamics and Differential Equations 24, #3 pp 427-481 (2012) (with A.N. Carvalho, J.A. Langa and A. Rodríguez-Bernal)

56. "The Neumann problem in thin domains with very highly oscillatory boundaries" (doi: 10.1016/j.jmaa.2013.02.061)
Journal of Mathematical Analysis and Applications 404, #1 pp 86-104 (2013) (with M.C. Pereira).

57. "Rate of convergence of global attractors of some perturbed reaction-diffusion problems"
Topological Methods in Nonlinear Analysis 41 (2), pp. 229-253 (2013) (with F.D.M. Bezerra and A.N. Carvalho)

58. "Spectral stability results for higher order operators under perturbations of the domain" (doi:10.1016/j.crma.2013.10.001)
C. R. Acad.Sci.Paris, Ser.I 351(2013)725–730 (with Pier D. Lamberti)

59. "Thin domains with doubly oscillatory boundary"   (doi:10.1002/mma.2875/pdf)
Mathematical Methods in Applied Science 37, #2, pp.158-166 (2014) (with Manuel Villanueva-Pesqueira)

60. "Stability estimates in $H^1_0$ for solutions of elliptic equations in varying domains" (doi:10.1002/mma.2948)
Mathematical Methods in Applied Science, 37, #2, pp.180-186 (2014) (with Gerassimos Barbatis)

61. "Estimates on the distance of inertial manifolds" (doi:10.3934/dcds.2014.34.3921)
Discrete and Continuous Dynamical Systems A 34, Vol 10 pp. 3921-3944 (2014) (with Esperanza Santamaría)

62. "Locally periodic thin domains with varying period" ( Locally periodic thin domains with varying periodo doi:10.1016/j.crma.2014.03.014)
C.R. Acad. Sci. Paris, Ser. I 352 pp. 397-403 (2014) (with Manuel Villanueva-Pesqueira)

63. "Asymptotic behavior of degenerate logistic equations" (doi:10.1016/j.jde.2015.07.028)
Journal of Differential Equations 259, #11 pp 6368-6398 (2015)(with R. Pardo and A. Rodríguez-Bernal)

64. "Unfolding operator method for thin domains with a locally periodic highly oscillatory boundary" (http://epubs.siam.org/doi/10.1137/15M101600X)
SIAM Journal of Mathematical Analysis 48-3, pp. 1634-1671, (2016) (with Manuel Villanueva-Pesqueira)

65. "Thin domains with non-smooth oscillatory boundaries" (http://dx.doi.org/10.1016/j.jmaa.2016.08.039)
Journal of Mathematical Analysis and Applications 446, #1 pp. 130-164 (2017)   (with Manuel Villanueva-Pesqueira)

66. "Higher order elliptic operators on variable domains. Stability results and boundary oscillations for intermediate problems" (https://doi.org/10.1016/j.jde.2017.05.011)
Journal of Differential Equations 263, #7 pp 4222-4266 (2017) (with Pier Domenico Lamberti)

67. "Distance of attractors of reaction-diffusion equations in thin domains" (https://doi.org/10.1016/j.jde.2017.06.023)
Journal of Differential Equations 263, #9 pp 5459-5506 (2017) (with Esperanza Santamaría)

68. "Spectral analysis of the biharmonic operator subject to Neumann boundary conditions on dumbbell domains" (https://link.springer.com/article/10.1007/s00020-017-2391-9)
Integral Equations and Operator Theory 89, Issue 3 pp 377-408 (2017) (with Francesco Ferrareso and Pier Domenico Lamberti)

69. "Boundary homogenization for a triharmonic intermediate problem" ( http://onlinelibrary.wiley.com/wol1/doi/10.1002/mma.4025/full )
Mathematical Methods in Applied Science 41, Issue 3 pp 979-985 (2018) (with Francesco Ferrareso and Pier Domenico Lamberti)

70. "C^{1,\theta}-Estimates on the distance of inertial manifolds" (https://doi.org/10.1007/s13348-018-0227-9)
Collectanea Mathematica 69, pp:315-336 (2018) (with Esperanza Santamaría)

71. "Semilinear elliptic equations in thin regions with terms concentrating on oscillatory boundaries" (https://doi.org/10.1016/j.camwa.2018.09.056)
Computers and Mathematics with Applications 77, pp 536-554 (2019) (with Ariadne Nogueira and Marcone C. Pereira)

72. "Nonlinear elliptic equations with concentrating reaction terms at an oscillatory boundary" (http://dx.doi.org/10.3934/dcdsb.2019079)
Discrete and Continuous Dynamical Systems 24 (8) pp: 4217-4246, (2019) (with Ariadne Nogueira and Marcone C. Pereira)

73. "Elliptic and parabolic problems in thin domains with doubly oscillatory boundary"
Communications in Pure and Applied Analysis 19 (4) (2020) (with Manuel Villanueva-Pesqueira)

Preprints:

1. "The p-Laplacian equation in thin domains: The unfolding approach"
Submitted (with Jean Carlos Nakasato and Marcone C. Pereira)