Guardado en:
Detalles Bibliográficos
Autores principales: Monreal, Javier, Kowalczyk, Michał
Formato: Preprint
Publicado: 2024
Materias:
Acceso en línea:https://arxiv.org/abs/2408.14413
Etiquetas: Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
Tabla de Contenidos:
  • In this article we study a coupled system of differential equations with Allen-Cahn type non-linearity. Motivated by physical phenomena one of the unknowns in the system is accompanied by a singular perturbation parameter $ε^2$ . By employing variational techniques, we establish the existence of solutions for all values of $ε$ and get results on their qualitative properties, including regularity. Additionally, we analyse the behaviour of solutions as $ε {\to} 0$, demonstrating their pointwise convergence to the solution of the problem for $ε = 0$. We establish the uniqueness of this solution modulo translations. Additionally, in the final section, through an appropriate change of scale, we relate this problem and the second Painlevé equation.