Asymptotic behaviour of solutions to some pseudoparabolic equations
نویسندگان
چکیده
The aim of this paper is to investigate the behavior as t ! 1 of solutions to the Cauchy problem u t ? u t ? u ? (b; ru) = r F (u); u(x; 0) = u 0 (x), where > 0 is a xed constant, t 0, x 2 IR n. First, we prove that if u is the solution to the linearized equation, i.e with rF(u) 0, then u decays like a solution for the analogous problem to the heat equation. Moreover, the long time behavior of u is described by the heat kernel. Next, analogous results are established for the nonlinear equation with some assumptions imposed on F , p, and the initial condition u 0 .
منابع مشابه
Initial-boundary Value Problems for Nonlinear Pseudoparabolic Equations in a Critical Case
We study nonlinear pseudoparabolic equations, on the half-line in a critical case, ∂t(u− uxx)− αuxx = λ|u|u, x ∈ R, t > 0, u(0, x) = u0(x), x ∈ R, u(t, 0) = 0, where α > 0, λ ∈ R. The aim of this paper is to prove the existence of global solutions to the initial-boundary value problem and to find the main term of the asymptotic representation of solutions.
متن کاملTHE NONPOSinVITY OF SOLUTIONS TO PSEUDOPARABOLIC EQUATIONS
Conditions are given on the nonnegative data «jc) and g{x, t) such that solutions of the pseudoparabolic inequality P[u] =» (L I)u, + Lu < 0 in Dx (0, t)
متن کاملError estimation for nonlinear pseudoparabolic equations with nonlocal boundary conditions in reproducing kernel space
In this paper we discuss about nonlinear pseudoparabolic equations with nonlocal boundary conditions and their results. An effective error estimation for this method altough has not yet been discussed. The aim of this paper is to fill this gap.
متن کاملHomogenization of a pseudoparabolic system
Pseudoparabolic equations in periodic media are homogenized to obtain upscaled limits by asymptotic expansions and two-scale convergence. The limit is characterized and convergence is established in various linear cases for both the classical binary medium model and the highly heterogeneous case. The limit of vanishing time-delay parameter in either medium is included. The double-porosity limit...
متن کاملThe comparison of optimal homotopy asymptotic method and homotopy perturbation method to solve Fisher equation
In recent years, numerous approaches have been applied for finding the solutions of functional equations. One of them is the optimal homotopy asymptotic method. In current paper, this method has been applied for obtaining the approximate solution of Fisher equation. The reliability of the method will be shown by solving some examples of various kinds and comparing the obtained outcomes with the ...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Appl. Math. Lett.
دوره 25 شماره
صفحات -
تاریخ انتشار 2012