Marcelo Cavalcanti

 Professor Marcelo Moreira Cavalcanti received his B.S., his M.S., and his Ph.D. degrees from the Federal University of Rio de Janeiro, in 1985, 1988, and 1995, respectively. He has been an Associated Professor in the Department of Mathematics at the State University of Maringá since 1989 up to 2015 and he is currently a Full professor at the same university. The main focus of his research is the study of the behavior of the energy of distributed systems. To explain more precisely the development of his research, consider a physical phenomenon which is described by a partial differential equation and, in addition, assume that there is an external or intrinsic mechanism (damping) acting on the system and which is responsible for the dissipation of its energy. The purpose of his study is to answer some questions related to the region where the damping must be acting in order to obtain the optimal decay rate of the energy. This subject was wisely described by one of the greatest contemporary scientists, Jacques Louis Lions (1928-2001) when he said: To "control" a system is to make it behave (hopefully) according to our "wishes," in a way compatible with safety and ethics, at the least possible cost. The systems considered here are distributed i.e., governed (modeled) by partial differential equations (PDEs) of evolution. Our "wish" is to drive the system in a given time, by an adequate choice of the controls from a given initial state to a final given state, which is the target. 

 According to an analysis of Essential Science Indicators from Thomson Reuters, the work of Dr. Marcelo Moreira Cavalcanti has entered the top 1% in the field of Mathematics. His record in this field includes 23 papers cited 199 times between January 1, 1999 and October 31, 2009. Find below a list of his selected papers: 

Cavalcanti, Marcelo M.; Corrêa, Wellington J.; Domingos Cavalcanti, Valéria N.; Tebou, Louis Well-posedness and energy decay estimates in the Cauchy problem for the damped defocusing Schrödinger equation.
J. Differential Equations 262 (2017), no. 3, 2521–2539. 

Cavalcanti, Marcelo M.; Corrêa, Wellington J.; Lasiecka, Irena; Lefler, Christopher Well-posedness and uniform stability for nonlinear Schrödinger equations with dynamic/Wentzell boundary conditions.
Indiana Univ. Math. J. 65 (2016), no. 5, 1445–1502. 

Cavalcanti, M. M.; Fatori, L. H.; Ma, T. F. Attractors for wave equations with degenerate memory.
J. Differential Equations 260 (2016), no. 1, 56–83. 

Cavalcanti, M. M.; Domingos Cavalcanti, V. N.; Guesmia, A. Weak stability for coupled wave and/or Petrovsky systems with complementary frictional damping and infinite memory.
J. Differential Equations 259 (2015), no. 12, 7540–7577. 

Cavalcanti, M. M.; Domingos Cavalcanti, V. N.; Komornik, V.; Rodrigues, J. H. Global well-posedness and exponential decay rates for a KdV-Burgers equation with indefinite damping.
Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), no. 5, 1079–1100. 

Bortot, César A.; Cavalcanti, Marcelo M. Asymptotic stability for the damped Schrödinger equation on noncompact Riemannian manifolds and exterior domains.
Comm. Partial Differential Equations 39 (2014), no. 9, 1791–1820. 

Cavalcanti, Marcelo M.; Dias Silva, Flávio R.; Cavalcanti, Valéria N. Domingos Uniform decay rates for the wave equation with nonlinear damping locally distributed in unbounded domains with finite measure.
SIAM J. Control Optim. 52 (2014), no. 1, 545–580. 

Bortot, C. A.; Cavalcanti, M. M.; Corrêa, W. J.; Domingos Cavalcanti, V. N. Uniform decay rate estimates for Schrödinger and plate equations with nonlinear locally distributed damping.
J. Differential Equations 254 (2013), no. 9, 3729–3764. 

Cavalcanti, Marcelo M.; Lasiecka, Irena; Toundykov, Daniel Wave equation with damping affecting only a subset of static Wentzell boundary is uniformly stable.
Trans. Amer. Math. Soc. 364 (2012), no. 11, 5693–5713. 

Cavalcanti, M. M.; Domingos Cavalcanti, V. N.; Fukuoka, R.; Soriano, J. A. Asymptotic stability of the wave equation on compact manifolds and locally distributed damping: a sharp result.
Arch. Ration. Mech. Anal. 197 (2010), no. 3, 925–964. 

Cavalcanti, M. M.; Domingos Cavalcanti, V. N.; Fukuoka, R.; Soriano, J. A. Asymptotic stability of the wave equation on compact surfaces and locally distributed damping—a sharp result.
Trans. Amer. Math. Soc. 361 (2009), no. 9, 4561–4580. 

Alves, Claudianor O.; Cavalcanti, Marcelo M. On existence, uniform decay rates and blow up for solutions of the 2-D wave equation with exponential source.
Calc. Var. Partial Differential Equations 34 (2009), no. 3, 377–411. 

Cavalcanti, Marcelo M.; Domingos Cavalcanti, Valéria N.; Lasiecka, Irena Well-posedness and optimal decay rates for the wave equation with nonlinear boundary damping—source interaction.
J. Differential Equations 236 (2007), no. 2, 407–459. 

Cavalcanti, M. M.; Domingos Cavalcanti, V. N.; Soriano, J. A.; Natali, F. Qualitative aspects for the cubic nonlinear Schrödinger equations with localized damping: exponential and polynomial stabilization.
J. Differential Equations 248 (2010), no. 12, 2955–2971. 

Cavalcanti, Marcelo M.; Domingos Cavalcanti, Valéria N.; Martinez, Patrick Existence and decay rate estimates for the wave equation with nonlinear boundary damping and source term.
J. Differential Equations 203 (2004), no. 1, 119–158. 

Cavalcanti, Marcelo Moreira; Oquendo, Higidio Portillo Frictional versus viscoelastic damping in a semilinear wave equation.
SIAM J. Control Optim. 42 (2003), no. 4, 1310–1324. 

Cavalcanti, M. M.; Cavalcanti, V. N. Domingos; Filho, J. S. Prates; Soriano, J. A. Existence and uniform decay of solutions of a parabolic-hyperbolic equation with 

nonlinear