Sufficient Conditions and Bounds Estimate of Blow-Up Time for a Fourth Order Parabolic Equation

• Lijing Zhao ^[1] ; Fushan Li ^[2]
  1. [1] Qufu Normal University

     Qufu Normal University

     China

     
  2. [2] Beijing Jiaotong University

     Beijing Jiaotong University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 3, 2022
• Idioma: inglés
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• Resumen

  • In this paper, we consider a fourth order parabolic equation with heat source function and homogeneous boundary conditions. We establish some sufficient conditions to guarantee that the solution u(x, t) blows up at finite time and obtain upper and lower bounds of the blow-up time by constructing the corresponding functionals. We generalize the heat source function and improve the proof of the critical inequality in the reference Philippin (Proc Am Math Soc 143(6):2507–2513, 2015).