- in memoriam: José Rodrigues Dias (1951-2023)
- in memoriam: Vladimir Goncharov (1962-2017)
- in memoriam: Graça Carita (1975-2016)
- Notícias
- Eventos
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Seminários
- The representation theory of the unitriangular group and other related groups
- On Computational Properties of Cauchy Problems
- Sets as Properties
- Artinian algebras and Jordan type
- Iterated Systems, Networks and Applications
- Isogeometric Analysis: mathematical and implementational aspects, with applications
- Sampling elusive populations: methods and applications
- Existence, non-existence and multiplicity results for some third-order periodic problems
- Convergence: what’s logic got to do with it?
- The Mathematics of Fires
- Old-age mortality deceleration and the modal age at death: insights from dynamic laws of adult mortality
- Stochastic differential equations models of animal growth and profit optimization in cattle raising
- Multidisciplinary approach for a real problem: modeling road traffic accidents
- The finite elements method and Freefem software
- DeepParticle: deep-learning invariant measure by minimizing Wasserstein distance on data generated from an interacting particle
- Kinematics: classification methods and combinatorial invariants for complex motion in biology
- Fractional Poisson Analysis in one Dimension
- Mathematics driven by epidemics
- ALMOST-POSITIONED NUMERICAL SEMIGROUPS
- A Delta approximation method on estimation for SDE mixed models
- Classificação de uma família de nós de Lorenz redutíveis
- Categoria de Lusternik-Schinrelmann e Grupos de Lie
- Euclides, Taylor, e a perspectiva esférica enquanto objecto matemático
- Time Series Clustering
- Condições geométricas para a existência e unicidade de projeção
- Sobre o volume de campos vetoriais
- Multiple criteria optimization: methods and applications
- Selective Base Revisions
- Nonautonomous attractors and bifurcation structures on nonautonomous families of flat topped tent maps
- Strongly nonlinear third order impulsive boundary value problems
- Solvability of second order coupled systems on the half-line
- Stochastic differential equations: brief introduction and profit optimization in fisheries
- Positioned Numerical Semigroups
- Tipo de Jordan de álgebras artinianas
- Complexidade em sistemas dinâmicos de baixa dimensão
- CFD Analysis in cerebral aneurysms
- Variational problems involving nonlocal supremal functionals
- Different Types of Stabilities in Times of Instability
- Non-linear systems of PDEs. Two examples from applications.
- Modelação de eventos extremos – uma introdução: aplicação ao decatlo e ao heptatlo atlético
- Comportamento assimptótico de soluções de problemas com valores na fronteira
- A característica de Euler de hipersuperfícies de espaços forma
- Brief introduction to stochastic differential equations and applications in Biology and Finance
- Sampling strategies in rural and urban settings in Africa - Looking from the sky
- Epidemiologia espácio-temporal no controlo da tuberculose
- Connectivity and Reliability of Mobile Ad-Hoc Networks
- Mathematical modeling, optimal control and complex network of epidemic models: case study of COVID-19 in Portugal
- Feature selection for marine species origin prediction
- Provas de Mestrado
- Provas de Doutoramento
- Apontadores
On Computational Properties of Cauchy Problems
In this talk, we will discuss recent quantitative versions of results on the asymptotic behavior of nonlinear semigroups generated by an accretive operator due to O. Nevanlinna and S. Reich [1] as well as H.-K. Xu [2]. These results rely on a particular assumption on the underlying operator introduced by A. Pazy [3] under the name of ‘convergence condition’. We will see various notions of a ‘convergence condition with modulus’ which provide the appropriate quantitative information on this condition in several different ways. These notions, as well as the extraction of quantitative information on the convergence results of Nevanlinna and Reich as well as Xu, were obtained through the use of logical techniques from proof mining [4,5], a subdiscipline of mathematical logic that aims at the extraction of new information from proofs of noneffective mathematical results. The extracted information will be in particular in the form of rates of convergence which depend on these moduli for the convergence condition. This is joint work with Nicholas Pischke.
Ref.:
[1] O. Nevanlinna and S. Reich. Strong convergence of contraction semigroups and of iterative methods for accretive operators in Banach spaces. Israel Journal of Mathematics, 32:44–58, 1979.
[2] H.-K. Xu. Strong asymptotic behavior of almost-orbits of nonlinear semigroups. Nonlinear Analysis: Theory, Methods & Applications, 46(1):135–151, 2001.
[3] A. Pazy. Strong convergence of semigroups on nonlinear contractions in Hilbert space. Journal of Mathematical Analysis and Applications, 34:1–35, 1978.
[4] U. Kohlenbach. Applied Proof Theory: Proof Interpretations and their Use in Mathematics. Springer Monographs in Mathematics. Springer-Verlag Berlin Heidelberg, 2008.
[5] N. Pischke. Logical metatheorems for accretive and (generalized) monotone set-valued operators. ArXiv e-prints, 2022. arXiv, math.LO, 2205.01788.
[6] P. Pinto and N. Pischke. On computational properties of Cauchy problems generated by accretive operators. ArXiv e-prints, 2023. arXiv, math.AP, 2301.06880.