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

# Next Seminar of 2018.1

## Fractional Cauchy problems with almost sectorial operators

#### Marduck Montoya Henao

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.

References
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
22/march/2018 Matheus Cheque Bortolan UFSC Impulsive dynamical systems: a baby course
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 - -