Time-periodic Parabolic Equations on Jrn

نویسندگان

  • DANIEL DANERS
  • Peter Hess
چکیده

to be exponentially stable and to apply these results to the study of change of stability in parameter dependent time-periodic parabolic problems. Here, !:::.. denotes the Laplacian in JRN and the weight-function lies in C~(JR, BUC(JRN)), the space of v-HOlder continuous and T -periodic functions taking values in the space of bounded uniformly continuous functions on JRN (v E (0, 1) and T > 0 fixed). Stability is to be understood either with respect to the Looor the L1-norm and initial conditions are taken in the spaces CO(JRN) and BUC(JRN) or Ll (JRN), respectively. As it turns out exponential stability will be a property which does not depend on the underlying space .. Our first characterization of exponential stability will be in terms of a quality that m may have or not as an inhomogeneity in the initial value problem

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On the Normal Semilinear Parabolic Equations Corresponding to 3D Navier-Stokes System

The semilinear normal parabolic equations corresponding to 3D Navier-Stokes system have been derived. The explicit formula for solution of normal parabolic equations with periodic boundary conditions has been obtained. It was shown that phase space of corresponding dynamical system consists of the set of stability (where solutions tends to zero as time t → ∞), the set of explosions (where solut...

متن کامل

The geometric properties of a degenerate parabolic equation with periodic source term

In this paper, we discuss the geometric properties of solution and lower bound estimate of ∆um−1 of the Cauchy problem for a degenerate parabolic equation with periodic source term ut =∆um+ upsint. Our objective is to show that: (1)with continuous variation of time t, the surface ϕ = [u(x,t)]mδq is a complete Riemannian manifold floating in space RN+1and is tangent to the space RN at ∂H0(t); (2...

متن کامل

Time Averaging for Random Nonlinear Abstract Parabolic Equations

It is well known that the averaging principle is a powerful tool of investigation of ordinary differential equations, containing high frequency time oscillations, and a vast work was done in this direction (cf. [1]). This principle was extended to many other problems, like ordinary differential equations in Banach spaces, delayed differential equations, and so forth (for the simplest result of ...

متن کامل

On forced periodic solutions of superlinear quasi - parabolic problems ∗

We study the existence of periodic solutions for a class of quasi-parabolic equations involving the p-Laplacian (or any other nonlinear operators of similar class) perturbed by nonlinear terms and forced by rather irregular periodic in time excitations (including what we call abrupt changes). These equations may model problems for which, aside from the presence of the kind of nonlinear dissipat...

متن کامل

Large-time Behavior of Periodic Entropy Solutions to Anisotropic Degenerate Parabolic-hyperbolic Equations

We are interested in the large-time behavior of periodic entropy solutions in L to anisotropic degenerate parabolic-hyperbolic equations of second-order. Unlike the pure hyperbolic case, the nonlinear equation is no longer self-similar invariant and the diffusion term in the equation significantly affects the large-time behavior of solutions; thus the approach developed earlier based on the sel...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010