Abstract :
We study nonlinear nonlocal equations on a half-line in the subcritical case
∂tu +β|u|ρu+Ku = 0, x>0, t >0,
u(0, x) = u0(x), x > 0,
∂
j−1
x u(0, t) = 0, j= 1, . . . , M,
(0.1)
where β ∈ C, ρ ∈ (0,α). The linear operator K is a pseudodifferential operator defined by the inverse
Laplace transform with dissipative symbol K(p) = Eαpα, the number M = [α2
]. The aim of
this paper is to prove the global existence of solutions to the initial-boundary value problem (0.1)
and to find the main term of the large time asymptotic representation of solutions in the subcritical
case, when the time decay rate of the nonlinearity is less than that of the linear part of the equation.
2004 Elsevier Inc. All rights reserved
