My research interests lie primarily in partial differential equations, mathematical physics, and stochastic processes. In particular, I have focused on the study of the asymptotic behavior of the solutions to some nonlinear dispersive equations, and the relation between some nonlocal integro-differential equations of Volterra type and stochastic processes.
Long and short time behavior of non-local time subdiffusion equations (with V. Vergara), Accepted in Applied Mathematics and Optimization
Nonlocal in-time telegraph equation and telegraph processes with random time, (with F. Alegría and V. Poblete), Journal of Differential Equations 347 (2023) 310--347
Wellposedness of second order evolution equations, (with F. Poblete and V. Poblete) Complex Anal. Oper. Theory 17 (2023), no. 3, Paper No. 42, 26 pp
Global solutions to the time non-local Navier-Stokes equations in Rd (with J. Azevedo and A. Viana), Discrete and Continuous Dynamical Systems Ser. B, 27. no 5, 2515--2535. [arxiv]
Existence of solutions of the abstract Cauchy problem of fractional order (with J. Godoy Mesquita and H. Henríquez),. [Journal Of Functional Analysis 281 (2021), no 4, Paper No. 109028, 39 pp] [arxiv]
Large time behavior for the heat equation on Z, moments and decay rates (with L. Abadías, J. Gonzalez and P. Miana). Journal of Mathematical Analysis and Applications, 500. (2021) no 2, Paper No. 125137, 25 pp [arxiv]
On local energy decay for large solutions of the Zakharov-Kuznetsov equation (with A. Méndez, C. Muñoz and F. Poblete), Comm. Partial Differential Equations 46 (2021), no. 8, 1440–1487. [arxiv]
Non-local in time telegraph equations and very slowly growing variances (with F. Alegría), Proc. Amer. Math. Soc. 149 (2021), no. 5, 2067–2080. [arxiv]
Existence of solutions for the semilinear abstract Cauchy problem of fractional order (with H. Henríquez and V. Poblete) Fract. Calc. Appl. Anal. 24 (2021), no. 5, 1409–1444 [arxiv]
Asymptotic to systems with memory and non-local initial data (with J. Muñoz-Rivera, V. Poblete and O. Vera), Reviews in Mathematical. Physics 32 (2020), no. 5, 2050014, 27 pp [arxiv]
A non-local in time telegraph equation (with V. Vergara), Nonlinear Analysis. 193 (2020), 111411, 22 pp. [arxiv]
L∞-solutions for the ultra-slow reaction-diffusion equation (with A. Viana), Math. Methods Appl. Sci. 42 (2019), no. 18, 6205–6215.
The scattering problem for Hamiltonian ABCD Boussinesq systems in the energy space (with K. Chulkwnag, C. Muñoz and F. Poblete). J. Math. Pures Appl. (9) 127 (2019), 121–159.
Fundamental solutions and decay of fully non-local problems (with V. Vergara), Discrete Contin. Dyn. Syst. 39 (2019), no. 1, 639–666, pdf.
Strong solutions of a neutral type equation with finite delay, (with F. Poblete and V. Poblete) J. Evol. Equ. 19 (2019), no. 2, 361–386.
Scattering in the energy space for Boussinesq equations (with C. Muñoz and F. Poblete). Comm. Math. Phys. 361 (2018), no. 1, 127–141
Existence of solutions for a class of abstract neutral differential equations, (with C. Cuevas, H. Henríquez and H. Soto) Discrete Contin. Dyn. Syst. 37 (2017), no. 5, 2455–2482.
Asymptotic behavior of non-local birth-death processes (with F. Alegría), In preparation.