|Address|| Department of Mathematics,
17 University Ave. Ste 1701
San Juan PR, 00925-2537
|Office||NCN II C-124|
|Telephone||(787) 764-0000 88270|
EducationPhD, Université de Franche-Comté, France., 1992
Research InterestsAnálisis Funcional; Semigrupos de Operadores; Ecuaciones de Evolución; Ecuaciones Diferenciales Parciales
- (with C. Lizama and M. Warma) Existence, regularity and representation of solutions of fractional wave equations. Electronic J. Differential Equations, Vol. 2017 (2017), No. 222, pp. 142.
- (with Yevhen Zelenyuk) Right ideal decompositions of G∗. Topology and Applications. 210 (2016), 90-96.
- (with M. Warma) On the interior approximate controllability of fractional wave equations. Discrete Contin. Dyn. Syst. 36 (2016), no. 7, 3719-3739.
- (with C. Lizama and M. Warma) Existence, regularity and representation of solutions of fractional diffusion equations. Adv. Differential Equations 21 (2016), no. 9-10, 837-886.
- (with Y. Zelenyuk) Discrete subsets and convergent sequences in topological groups. Topology and Applications. 191 (2015), 137-142.
- (with C. Lizama and M. Warma) Spectral criteria for solvability of boundary value problems and positivity of solutions of time-fractional differential equations. Abstract and Applied Analysis, 2013, Art. ID 614328.
- (with P. J. Miana and L. S ́anchez Lajusticia) Sharp extension for convoluted solutions of abstract Cauchy problems. Integral Equations Op- erator Theory, 77 (2013), 211-241.
- (with Y. Zelenyuk) Strongly complete almost maximal left invariant topologies on groups. Topology and Applications, 160 (2013), 1494- 1500.
- (with C. Lizama and M. Warma) Asymptotic behavior of fractional order semilinear evolution equations. Differential Integral Equations, 26 (2013), 757-780.
- (with C. Lizama) On a connection between powers of operators and fractional Cauchy problems. Journal of Evolution Equations, 12 (2012), 245-265.
- (with C. Lizama) A characterization of periodic solutions for time- fractional differential equations in UMD spaces and applications. Math. Nachr. 284 (2011), 494-506.
- (with C. Lizama and P. J. Miana) Algebra homomorphisms defined via convoluted semigroups and cosine functions. J. Funct. Anal. 257 (2009), no. 11, 3454–3487.
- (with C. Lizama and V. Poblete) Periodic Solutions of Integro-differential Equations in Vector-valued Function Spaces. J. Differential Equations. 246 (2009), 1007-1037.
- (with R. Chill and M. Warma) Generation of cosine families on Lp(0, 1) by elliptic operators with Robin boundary conditions. In: H. Amann, W. Arendt, M. Hieber, F. Neubrander, S. Nicaise, J. von Below (Eds.): ”Functional Analysis and Evolution Equations - The Gunter Lumer Vol- ume”, 113-130, Birkh ̈auser, 2008.
- (with C. Lizama) Mild solutions of abstract differential equations. In: H. Amann, W. Arendt, M. Hieber, F. Neubrander, S. Nicaise, J. von Be- low (Eds.): ”Functional Analysis and Evolution Equations - The Gunter Lumer Volume”, 371-388, Birkh ̈auser, 2008.
- (with C. Lizama) H ̈older continuous solutions for integro-differential equations and maximal regularity. J. Differential Equations, 230(2006), 634-660.
- (with M. Warma) The wave equation with Wentzell-Robin boundary conditions on Lp-spaces.J. Differential Equations, 229 (2006), 680-697.
- (with C. Lizama) Periodic solutions of second order differential equations in Banach spaces. Math. Z. 253 (2006), 489-514.
- (with C. Müller and P. Vieten) The Hille-Yosida theorem for local convoluted semigroups. Proc. Edinburgh Math. Soc.,46 (2003), 395-413.
- The Laplace transform and the ascent method for abstract wave equations. J. Differential Equations, 122 (1995), 27-47.
- (with W. Arendt and O. El-Mennaoui) Local integrated semigroups: evolution with jumps of regularity. J. Math. Anal. Appl., 186 (1994), 572-595.
Grants and Awards
- Co-PI: Air Force Office of Scientific Research [2014-2017]: Dynamics, Control and Numerics for Fractional Partial Differential Equations (PI: M. Warma).
- Convenio de Cooperaci ́on Internacional (CONICYT) Grant # 7060064 (Chile): 2006.
- Convenio de Cooperaci ́on Internacional (CONICYT) Grant # 7050008 (Chile): 2005.
- Convenio de Cooperaci ́on Internacional (CONICYT) Grant # 7010675 (Chile): 2002-2004.
Additional InformationPremio de Excelencia Academica, UPR Rio Piedras, 1999