• 1
  • 1
  • 2
  • 6
  • 5
  • 6
  • 3
  • 4
IPM
30
YEARS OLD

“School of Mathematics”

Back to Papers Home
Back to Papers of School of Mathematics

Paper   IPM / M / 16332
School of Mathematics
  Title:   Blow-up phenomenon and the exact blow-up time for a class of pseudo-parabolic equations with a nonlocal source
  Author(s):  Khadijeh Baghaei (joint with A. Khelghati)
  Status:   Published
  Journal: Math. Methods Appl. Sci.
  Year:  2020
  Pages:   DOI: 10.1002/mma.6841
  Supported by:  IPM
  Abstract:
his paper deals with the blow‐up phenomenon to the following quasi‐linear pseudo‐parabolic equation with nonlocal source: u t − Δ u t − ∇ · ( - ∇ u - 2 q ∇ u ) = u p ( x , t ) ∫ Ω K ( x , y ) u p + 1 ( y , t ) d y , x , y ∈ Ω , t > 0 , where Ω ⊆ ℝ n , n ≥ 3 , is a bounded domain with smooth boundary. Here, 0 < q ≤ p and K(x,y) is an integrable real‐valued function. We show that for q < p, the blow‐up occurs in finite time with suitable initial data and arbitrary positive initial energy. We also state some key results based on the conception of limiting the energy function in the case of nonnegative initial energy. Besides, we obtain the exact blow‐up time under some certain conditions.

Download TeX format
back to top
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
scroll left or right