Well-Posedness of Mild Solutions for Superdiffusion Equations with Spatial Nonlocal Operators

• Xuan-Xuan Xi ^[1] ; Yong Zhou ^[2] ; Mimi Hou ^[3]
  1. [1] Xiangtan University

     Xiangtan University

     China

     
  2. [2] Macau University of Science and Technology

     Macau University of Science and Technology

     RAE de Macao (China)

     
  3. [3] Huaibei Normal University

     Huaibei Normal University

     China

     

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 5, 2024
• Idioma: inglés
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• Resumen

  • In this paper, we study the well-posedness for a class of semilinear superdiffusion equations with spatial nonlocal operators. We first establish the Gagliardo–Nirenberg inequality in -Bessel potential spaces. Based on this, the well-posedness results of local and global mild solution for corresponding linear problem are obtained via apriori estimates. We also obtain the well-posedness results for the nonlinear problem under different conditions. These conclusions are mainly based on the Mihlin–Hörmander’s multiplier estimates, embedding theorem and fixed point theory.