Last Update: 10:75 - Wednesday - May 23rd 2018.

Next Seminar of 2018.1

Fractional Cauchy problems with almost sectorial operators

Marduck Montoya Henao

Doutorado - UFSC
The goal of this seminar is to discuss the needed tools to ensure the existence and uniqueness of some Cauchy problems described by the abstract differential equation: \begin{equation*}\label{NL} \left\lbrace \begin{array}{l} _cD_{t}^{\alpha}u(t)+Au(t)=0,\ t>0,\\ u(0)=u_{0}\in X, \end{array} \right. \end{equation*} with $_cD_{t}^{\alpha}$ denoting the Caputo derivative of order $\alpha\in(0,1)$ and $A\colon D(A)\subset X\rightarrow X$ an almost sectorial operator. Note that, as discussed in [1,2], almost sectorial operators have some deficiencies on the estimates of its resolvent operator, and the generated semigroup behaves singularly at $t=0$. This new behavior gives rise to a quite rich discussion about this new class of operators, with together with the fractional derivation theory, justify the study of this problem (see [3] for more details). This work was done under the advisement of Prof. Paulo Mendes de Carvalho Neto.

1. J. M. Arrieta, A. N. Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J. Differential Equations, 231 (2006) 551--597.
2. J. M. Arrieta, A. N. Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains II. The limiting problem, J. Differential Equations, 247 (2009) 174--202.
3. R-N. Wang, D-H. Chen and T-J. Xiao, Abstract fractional Cauchy problems with almost sectorial operators, Journal of Differential Equations, 252 (2012) 202--235.

Room: Room 202 - Maths Department       Date: Thursday - May 24th, 2018        Time: 14:00 to 15:00

Calendar for 2018.1

The lectures of the SED take place usually on Thursdays from 13:30 to 15:30 at Room 202 of the Maths Department building at UFSC.

Date Lecturer Institute Title File
15/march/2018 Jáuber Cavalcante de Oliveira UFSC Existence of strong solutions to the Navier-Stokes equations with nonlinear dissipation W3Schools
22/march/2018 Matheus Cheque Bortolan UFSC Impulsive dynamical systems: a baby course W3Schools
29/march/2018 - - -
5/april/2018 Vinícius Viana Luiz Albani UFSC Jump Diffusion Parameter Estimation in Finance
12/april/2018 Fábio Junior Margotti UFSC Electrical Impedance Tomography applied to a real problem of oil extraction
19/april/2018 Marcio Jorge da Silva UEL Viscoelastic and Thermoelastic effects in beams of Timoshenko type
26/april/2018 Francis Felix Cordova Puma UFSC - Blumenau Decay of solutions for a mixture of thermoelastic solids
03/may/2018 Paulo Amorim UFRJ Reaction-diffusion and individual-based models for ant movement
10/may/2018 Cleverson Roberto da Luz UFSC Optimal decay rates for a Timoshenko system in bounded domain
17/may/2018 Edson Cilos Vargas Júnior Doutorado - UFSC Structural damped $\sigma$-evolution equation with fast oscillation I
24/may/2018 Marduck Montoya Henao Doutorado - UFSC Fractional Cauchy problems with almost sectorial operators
31/may/2018 National Holiday
7/june/2018 Maíra Fernandes Gauer Palma UFSC - Joinville -
14/june/2018 Ruy Coimbra Charão UFSC -
21/june/2018 Eleomar Cardoso Júnior UFSC - Blumenau -
28/june/2018 Closing - -

About the Seminars

The SED is composed by weekly lectures, presented by researches on the fields of Differential Equations and Nonlinear Dynamical Systems, and its goal is to inform researchers and Math graduate students about the recent research developments on these areas.

Graduate Department

Head Chief: Prof. Ruy Coimbra Charão
E-mail: ruy.charao at ufsc.br

First Assistant: Elisa Barbosa Amaral
E-mail: elisa.amaral at ufsc.br

Second Assistant: Érica Flores
E-mail: erica.flores at ufsc.br

Current Coordinator

Prof. Matheus Cheque Bortolan

E-mail: m.bortolan at ufsc.br
Home: mtm.ufsc.br/~bortolan
Phone: +55 (48) 3721-3699

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