Study of a nonlocal Chafee-Infante equation using semigroup theory

• Autores: Yessica Yulieth Julio Pérez
• Directores de la Tesis: Tomás Caraballo Garrido (dir. tes.), Alexandre Nolasco de Carvalho (dir. tes.)
• Lectura: En la Universidad de Sevilla ( España ) en 2024
• Idioma: inglés
• Número de páginas: 107
• Enlaces
  • Tesis en acceso abierto en: Idus
• Resumen

  • In this work, we focus on analyzing non-local and quasilinear variations of the Chafee-Infante problem, including one variant with delay. To tackle these challenges, we use a time reparameterization, enabling us to reframe them as semilinear problems. We present an abstract approach to semilinear equations, offering broad applicability and facilitating extension to diverse models.

    Our analysis encompasses several key aspects. Firstly, we address the existence (possibly non-unique) of mild solutions and their regularity, contingent upon an appropriate modulus of continuity on the nonlinearity. Additionally, we explore comparison results utilizing the variation of constants formula.

    Leveraging these comparisons, we establish global existence, under the supplementary condition that the nonlinearity adheres to a structural criterion and is complemented by uniform bounds provided that the nonlinearity exhibits dissipative behavior. Furthermore, we establish the existence of global/pullback attractor for the associated multivalued semigroup/process.