Resolubilidade de problemas lineares de cauchy em espaços de fréchet e um modelo de kaldor com retardo
- Autores: Alex Pereira da Silva
- Directores de la Tesis: Alexandre Nolasco de Carvalho (dir. tes.), Tomás Caraballo Garrido (dir. tes.)
- Lectura: En la Universidad de Sevilla ( España ) en 2019
- Idioma: español
- Tribunal Calificador de la Tesis: Paulo L. Dattori da Silva (presid.), Everaldo de Mello Bonotto (secret.), Pedro Marín-Rubio (voc.), José Antonio Langa Rosado (voc.), Rafael Fernando Barostichi (voc.)
- Programa de doctorado: Programa de Doctorado en Matemáticas por la Universidad de Sevilla
- Materias:
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- Resumen
The long-run aim of this thesis is to solve delay differential equations with infinite delay of the type d/dt u (t)=Au(t)+∫_(-∞)^t▒〖u(s)k (t-s)ds+ "f" ("t,u(t)" ) 〗 on Fréchet spaces under an extended theory of groups of linear operators; where A is a linear operator, k(s) ⩾ 0 satisfies ∫_0^∞▒〖k(s)ds=1〗 and f is a nonlinear map.
In order to pursue such a goal we study a discrete delay model which explains the natural economic fluctuations considering how economic stability is affected by the role of the fiscal and monetary policies and a possible government inefficiency concerning its fiscal policy decision-making. On the other hand, we start to develop such an extended theory by considering linear Cauchy problems associated to a continuous linear operator on Fréchet spaces, for which we establish necessary and sufficient conditions for generation of a uniformly continuous group which provides the unique solution. Further consequences arises by considering pseudodifferential operators with constant coefficients defined on a particular Fréchet space of distributions, namely 〖FL〗_loc^2 , and special attention is given to the distributional solution of the heat equation on 〖FL〗_loc^2 loc for all time, which extends the standard solution on Hilbert spaces for positive time.
