Singular perturbation of a nonlinear time-dependent problem in hilbert space

Abstract

The convergence of the solution of the nonlinear singular perturbation problem U˝'J + aU´ { + e2AnUε £ + g(AUε e) + h(t, A)]f(A)Uε e = 0, C/ε e(0) = x0, f/´ €'(0) = zi for ϵ > 0 to the solution of the degenerate problem (ϵ - 0) is studied. Here a [math001] 0 is a constant and A is a (generally unbounded) self- adjoint linear operator in Hilbert space. The problem is nonlocal, nonlinear, and time dependent because of g(‖AU‖)f(A)U and h(t,A). The existence of solutions is proven simultaneously with asymptotic behaviour.

Keywords:

• AMS(MOS): 34E15, 35B25

Keywords:

• Singular perturbations
• nonlinear
• nonlocal
• initial value problem
• time dependent

^*Partially supported by TGRC-KOSEF

^*Partially supported by TGRC-KOSEF

Notes

^*Partially supported by TGRC-KOSEF