Works in Preparation
- R. Folino, C. A. Hernández Melo, L. F. López Ríos, R. G. Plaza, Nonlinear stability of stationary reaction diffusion-degenerate Nagumo fronts.
Submitted Preprints
- A. Capella, C. Melcher, L. Morales, R. G. Plaza, Stability of moving Néel walls in ferromagnetic thin films. Preprint, 2024. Submitted to Z. Angew. Math. Phys. [ARXV]
- A. Naumkina, R. G. Plaza, Orbital instability of
periodic waves for generalized Korteweg-de Vries-Burgers
equations with a source. Preprint, 2024. [ARXV]
- F. Angeles, R. G. Plaza, J. M. Valdovinos, Dissipative
structure of higher order systems in several space
dimensions. Preprint, 2024. [ARXV]
- R. G. Plaza, J. M. Valdovinos, Global decay of
perturbations of equilibrium states for one-dimensional
heat conducting compressible fluids of Korteweg type. Preprint,
2023. Submitted to J. Differ. Equ. [ARXV]
- C. Lattanzio, C. Mascia, R. G. Plaza, C. Simeoni, Analysis
and numerics of the propagation speed for hyperbolic
reaction-diffusion models. Preprint, 2019.
Submitted to D. Donatelli (ed.), Partial Differential
Equations: Ambitious Mathematics for Real-Life Applications,
SEMA-SEMAI Series, Springer-Verlag. [ARXV|PRE]
- C. Lattanzio, C. Mascia, R. G. Plaza, C. Simeoni, Spectral stability of traveling fronts for nonlinear hyperbolic equations of bistable type. Preprint, 2018. Submitted to D. Donatelli (ed.), Partial Differential Equations: Ambitious Mathematics for Real-Life Applications, SEMA-SEMAI Series, Springer-Verlag. [ARXV|PRE]
Publications in Refereed Journals
- A. Capella, C. Melcher, L. Morales, R. G. Plaza, Nonlinear
stability of static Néel walls in ferromagnetic thin
films. Arch. Ration. Mech. Anal. 248 (2024),
no. 119, 1-47. [ARXV|DOI]
- R. G. Plaza, D. Zhelyazov, Well-posedness and decay structure of a quantum hydrodynamics system with Bohm potential and linear viscosity. J. Math. Phys. 65 (2024), 081508, 1-35. [ARXV|DOI]
- R. Folino, A. Naumkina, R. G. Plaza, Instability of
periodic waves for the Korteweg-de Vries-Burgers equation
with monostable source. Phys. D 467 (2024), 134234,
1-10. [ARXV|DOI]
- E. Álvarez, J. Angulo Pava, R. G. Plaza, Orbital instability of periodic waves for scalar viscous balance laws. J. Evol. Equ. 24 (2024), art. no. 7, 1-35. [ARXV|DOI]
- R. Folino, R. G. Plaza, D. Zhelyazov, Spectral stability of weak dispersive shock profiles in a quantum hydrodynamics system with nonlinear viscosity. J. Differ. Equ. 359 (2023), 330-364. [ARXV|DOI]
- J. F. Leyva, L. F. López Ríos, R. G. Plaza, Spectral
stability of monotone traveling fronts for
reaction diffusion-degenerate Nagumo equations. Indiana
Univ. Math. J. 71 (2022), no. 6, 2335-2376. [ARXV|DOI]
- R. Folino, R. G. Plaza, D. Zhelyazov, Spectral stability of small-amplitude dispersive shocks in quantum hydrodynamics with viscosity. Comm. Pure Appl. Anal. 21 (2022), no. 12, 4019-4040. [ARXV|DOI]
- E. Álvarez, R. Murillo, R. G. Plaza, Spectral instability of small-amplitude periodic waves for hyperbolic non-Fickian diffusion advection models with logistic source. Math. Model. Nat. Phenom. 17 (2022), art. no. 13, 1-25. [ARXV|DOI]
- R. G. Plaza, J. M. Valdovinos, Dissipative structure of one-dimensional isothermal compressible fluids of Korteweg type. J. Math. Anal. Appl. 514 (2022), no. 2, 126336. [ARXV|DOI]
- R. Folino, L. F. López Ríos, R. G. Plaza, Long-time behavior of solutions to the generalized Allen-Cahn model with degenerate diffusivity. Nonlinear Differ. Equ. Appl. 29 (2022), art. no. 45, 1-38. [ARXV|DOI]
- R. G. Plaza, F. Vallejo, Stability of classical shock fronts for compressible hyperelastic materials of Hadamard type. Arch. Ration. Mech. Anal. 243 (2022), no. 2, 943-1017. [ARXV|DOI]
- J. Angulo Pava, R. G. Plaza, Unstable kink and anti-kink profiles for the sine-Gordon equation on a -junction graph. Math. Z. 300 (2022), no. 3, 2885-2915. [ARXV|DOI]
- J. Angulo Pava, R. G. Plaza, Instability theory of kink and anti-kink profiles for the sine-Gordon equation on Josephson tricrystal boundaries. Phys. D 427 (2021), 133020, 1-12. [ARXV|DOI]
- E. Álvarez, R. G. Plaza, Existence and spectral instability of bounded spatially periodic traveling waves for scalar viscous balance laws. Quart. Appl. Math. 79 (2021), no. 3, 493-544. [ARXV|DOI]
- R. Folino, R. G. Plaza, M. Strani, Long time dynamics of solutions to p-Laplacian diffusion problems with bistable reaction terms. Discrete Cont. Dyn. Syst. 41 (2021), no. 7, 3211-3240. [ARXV|DOI]
- J. Angulo Pava, R. G. Plaza, Instability of static solutions of the sine-Gordon equation on a -junction graph with -interaction. J. Nonlinear Sci. 31 (2021), no. 3, art. 50, 1-32. [ARXV|DOI]
- R. Folino, R. G. Plaza, M. Strani, Metastable patterns
for a reaction-diffusion model with mean curvature-type
diffusion. J. Math. Anal. Appl. 493 (2021), no. 1,
124455. [ARXV|DOI]
- R. Folino, C. A. Hernández Melo, L. F. López Ríos, R. G.
Plaza, Exponentially slow motion of interface layers for
the one-dimensional Allen-Cahn equation with nonlinear
phase-dependent diffusivity. Z. Angew. Math. Phys. 71
(2020), no. 4, pp. 132 (1-25) [ARXV|DOI|PRE]
- F. Angeles, C. Málaga, R. G. Plaza, Strict dissipativity of Cattaneo-Christov systems for compressible fluid flow. J. Phys. A 53 (2020), no. 6, pp. 065701 [ARXV|DOI]
- J. F. Leyva, R. G. Plaza, Spectral stability of traveling fronts for reaction diffusion-degenerate Fisher-KPP equations. J. Dyn. Diff. Equat. 32 (2020), no. 3, 1311-1342 [ARXV|DOI]
- D. Pera, C. Málaga, C. Simeoni, R. G. Plaza, On the efficient numerical simulation of heterogeneous anisotropic diffusion models of tumor invasion using GPUs. Rend. Mat. Appl. 40 (2019), no. 3-4, 233-255. [DOI|PRE]
- I. Padilla, R. G. Plaza, On the role of cancer cells' diffusion in the tumor growth paradox. Rend. Mat. Appl. 40 (2019), no. 3-4, 217-231. [ARXV|DOI|PRE]
- J. Angulo Pava, C. A. Hernández Melo, R. G. Plaza, Orbital
stability of standing waves for the nonlinear Schrödinger
equation with attractive delta potential and double power
repulsive nonlinearity. J. Math. Phys. 60 (2019), no.
7, 071501 [ARXV|DOI]
- R. G. Plaza, Derivation of a bacterial nutrient-taxis system with doubly degenerate cross-diffusion as the parabolic limit of a velocity jump process. J. Math. Biol. 78 (2019), no. 6, 1681-1711. [ARXV|DOI]
- C. Lattanzio, C. Mascia, R. G. Plaza, C. Simeoni, Kinetic
schemes for assessing stability of traveling fronts for
the Allen-Cahn equation with relaxation. Appl. Numer.
Math. 141 (2019), 234-247. [ARXV|DOI|PRE]
- J. A. Butanda, C. Málaga, R. G. Plaza, On the stabilizing effect of chemotaxis on bacterial aggregation patterns. Appl. Math. Nonlinear Sci. 2 (2017), no. 1, 157-172. [DOI|PRE]
- J. Angulo Pava, R. G. Plaza, Transverse orbital stability of periodic traveling waves for nonlinear Klein-Gordon equations. Stud. Appl. Math. 137 (2016), no. 4, 473-501. [DOI|PRE]
- C. Lattanzio, C. Mascia, R. G. Plaza, C. Simeoni, Analytical and numerical investigation of traveling waves for an Allen-Cahn model with relaxation. Math. Models Methods Appl. Sci. 26 (2016), no. 5, pp. 931-985. [ARXV|DOI]
- C. K. R. T. Jones, R. Marangell, P. D. Miller, R. G. Plaza, Spectral and modulational stability of periodic wavetrains for the nonlinear Klein-Gordon equation. J. Differ. Equ. 257 (2014), no. 12, pp. 4632-4703. [ARXV|DOI]
- J. F. Leyva, C. Málaga, R. G. Plaza, The effects of nutrient chemotaxis on bacterial aggregation patterns with non-linear degenerate cross diffusion. Phys. A 392 (2013), no. 22, pp. 5644-5662. [ARXV|DOI]
- C. K. R. T. Jones, R. Marangell, P. D. Miller, R. G. Plaza, On the stability analysis of periodic sine-Gordon traveling waves. Phys. D 251 (2013), no. 1, pp. 63-74 [ARXV|DOI]
- C. Málaga, A. A. Minzoni, R. G. Plaza, C. Simeoni, A chemotactic model for interaction of antagonistic microflora colonies: front asymptotics and numerical simulations. Stud. Appl. Math. 130 (2013) no. 3, pp. 264-294. [ARXV|DOI|PDF]
- R. G. Plaza, Lp-decay rates for perturbations of degenerate scalar viscous shock waves. J. Math. Anal. Appl. 382 (2011), no. 2, pp. 864-882. [DOI|PDF|PRE]
- T. Nguyen, R. G. Plaza, K. Zumbrun, Stability of radiative shock profiles for hyperbolic-elliptic coupled systems. Phys. D 239 (2010), no. 8, pp. 428-453. [ARXV|DOI|PDF]
- C. Lattanzio, C. Mascia, T. Nguyen, R. G. Plaza, K. Zumbrun, Stability of scalar radiative shock profiles. SIAM J. Math. Anal. 41 (2009), no. 6, pp. 2165-2206. [ARXV|DOI|PDF]
- G. Flores, R. G. Plaza, Stability of post-fertilization traveling waves. J. Differ. Equ. 247 (2009), no. 5, pp. 1529-1590. [DOI|PDF]
- R. G. Plaza, Multidimensional stability of martensite twins under regular kinetics. J. Mech. Phys. Solids 56 (2008), no. 5, pp. 1989-2018. [DOI|PDF]
- R. G. Plaza, A Sobolev-type inequality with applications. J. Ineq. Pure Appl. Math 8 (2007), no. 1, art. 2, 13 pp. [DOI|PDF|PRE]
- H. Freistühler, R. G. Plaza, Normal modes and nonlinear stability behaviour of phase boundaries in elastic materials. Arch. Ration. Mech. Anal. 186 (2007), no. 1, pp. 1-24. [DOI|PDF]
- R. G. Plaza, P. Padilla, F. Sánchez-Garduño, R. A. Barrio, P. K. Maini, The effects of growth and curvature in pattern formation. J. Dyn. Diff. Equat. 16 (2004), no. 4, pp. 1093-1121. [DOI|PDF]
- R. G. Plaza, K. Zumbrun, An Evans function approach to spectral stability of small-amplitude shock profiles. Discrete Cont. Dyn. Syst. 10 (2004), no. 4, pp. 885-924. [ARXV|DOI|PDF]
Conference Proceedings (Refereed)
- C. Lattanzio, C. Mascia, R. G. Plaza, C. Simeoni, Numerical
computation of the wave speed for hyperbolic
reaction-diffusion equations, in C. Parés et al.
(eds.), Proceedings of the XVIII International Conference on
Hyperbolic Problems: Theory, Numerics, Applications
(HYP2022). June 20 - 24, 2022. Málaga, Spain. Hyperbolic
Problems: Theory, Numerics, Applications, Volume II, SEMA
SIMAI Springer Series 35. Springer-Verlag, 2024. [DOI]
- C. K. R. T. Jones, R. Marangell, P. D. Miller, R. G. Plaza, On the spectral and modulational stability of periodic wavetrains for nonlinear Klein-Gordon equations. Proceedings of the XV International Conference on Hyperbolic Problems: Theory, Numerics, Applications (HYP2014). July 28 - August 1, 2014. IMPA, Rio de Janeiro, Brazil. Bull. Brazilian Math. Soc., New Series 47 (2016), no. 2, pp. 417-429. [DOI|PRE]
- R. G. Plaza, On the stability of degenerate viscous shock profiles. In F. Ancona, A. Bressan, P. Marcati, A. Marson (eds.), Hyperbolic problems: Theory, Numerics, Applications. Proceedings of the 14th International Conference in Hyperbolic Problems (Padova 2012). AIMS Series on Applied Mathematics Vol. 8, American Institute of Mathematical Sciences, 2014, pp. 857-864.[PDF]
- H. Freistühler, R. G. Plaza, Normal modes analysis of subsonic phase boundaries in elastic materials. In S. Benzoni-Gavage, D. Serre (eds.), Hyperbolic problems: Theory, Numerics, Applications. Proceedings of the 11th International Conference in Hyperbolic Problems (Lyon 2006). Springer-Verlag, 2008, pp. 841-847. [DOI|PDF]
Textbooks and Lecture Notes
- R. G. Plaza, Introduction to Mathematical Biology (in Spanish). In preparation.
- A. Capella, R. G. Plaza, Partial Differential Equations (in Spanish). In preparation.
- R. G. Plaza, Hyperbolic Systems of Conservation Laws (in Spanish). In preparation.
Theses
- R. G. Plaza, On the stability of shock profiles, Ph. D. Thesis, New York University, New York, 2003.
- R. G. Plaza, A free-boundary value problem for the stationary Navier-Stokes equations (in Spanish), B. Sc. Thesis, National University of México (UNAM), México, 1996.