SUT J. Math. 45 (1), 1-23, (January 2009) DOI: 10.55937/sut/1248706004
Rosa E. Cardiel-Cervantes, Pavel I. Naumkin
KEYWORDS: Neumann initial-boundary value problem, large time asymptotics, Pseudodifferential equation, 35Q40, 35Q35
Our goal is to study the global existence and large time asymptotic behavior of solutions to the Neumann initial-boundary value problem for the nonlinear nonlocal equation on a half-line
where the nonlinear term is , with , and is a pseudodifferential operator defined by the inverse Laplace transform
where . We prove that if the initial data for , then there exists a unique solution
for the inital-boundary value problem. We also obtain the large time asymptotic formulas for the solutions...