In this paper, the existence and uniqueness of generalized solution for the initial boundary value problems (1.6)~(1.9) of coupled ordinary differential equations and higher order parabolic equations are proved by means of the theory of nonlinear semigroup.
The second chapter studies the continuous model (2. 1. 1), under two cases: fixed case and random case, it obtains the local existence theorems of solutions for nonlinear evolutional equations with random migration perturbation, by utilizing the theorems of m -accretive operator as well as the nonlinear semigroup theory.
In this paper we consider the Cauchy problem for the system of gas dynamics with a viscosity term u_i+[p(v)]_x=μu_(xx),v_t-u_x=0. By means of the theory of nonlinear semigroups, we have proved the existence and uniqueness of the generalized solution of this problem.
The global fast dynamics for the generalized symmetric regularized long wave equation with damping term is considered. The squeezing property of the nonlinear semi-group associated with this equation and the existence of exponential attractor are proved. The upper bounds of its fractal dimension are also estimated.
This paper discussed the continuity conditions of duality mapping F(x) and obtains several equivalent reations between F(x) single-valued uniformly continuous, uniformly lower semi-continuous and support function uniformly continuous.
This paper structures the strong solution of the initial boundary value problem of nonstationary flow of incompressible non-Newtonian fluids,using non-linear semigroup theory.
By virtue of nonlinear semigroup theory, energy-perturbed approach and exponential multiplier method, it is shown that the vibration of the beam under the proposed control action decays exponentially or in negative power of time t as t → ∞.
We also obtain similar results for accretive operators that are not necessarily m-accretive, and deduce invariance and order-preserving criteria for nonlinear semigroups.
Under some nonlinear boundary feedback controls, the nonlinear semi-group theory is used to show the well-posedness for the correspnding closed loop system.