Existence and global behavior of solutions to fractional p-Laplacian parabolic problems
Texas State University, Department of Mathematics
First, we discuss the existence, the uniqueness and the regularity of the weak solution to the following parabolic equation involving the fractional p-Laplacian, ut + (-∆)spu + g(x, u) = ƒ(x, u) in QT := Ω x (0, T), u = 0 in ℝN \ Ω x (0, t), u(x, 0) = u0(x) in ℝN. Next, we deal with the asymptotic behavior of global weak solutions. Precisely, we prove under additional assumptions on ƒ and g that global solutions converge to the unique stationary solutions as t → ∞.
p-Fractional operator, Existence and regularity of weak solutions, Asymptotic behavior of global solutions, Stabilization
Giacomoni, J., & Tiwari, S. (2018). Existence and global behavior of solutions to fractional p-Laplacian parabolic problems. <i>Electronic Journal of Differential Equations, 2018</i>(44), pp. 1-20.