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Asyptotics for the Solution of Euler-Bernoulli Type Eqution

Author: PanTing
Tutor: XueRuYing
School: Zhejiang University
Course: Basic mathematics
Keywords: Euler-Bernoulli equation Young’s inequality Existence Large time asymptotic behavior
CLC: O175.8
Type: Master's thesis
Year: 2010
Downloads: 4
Quote: 0
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Abstract


In this paper,the existence and uniqueness and the large time asymptotic behavior of the solution for the Euler-bernoulli equation with initial-value conditions are considered. By using the theory of Sobolev spaces and the contraction mapping principle,we proved that the Euler-bernoulli equation possesses a unique global solu-tion u∈C([0,∞);Lp(Rn)∩L1,a (Rn))∩C((0,∞);L∞(Rn)) when the initial data u0,u1∈Lp(R)∩L1.a(R)(in whichσ>1,a∈(0,1],p>σ)and its norm‖u0‖L1.a+‖u0‖Lp+‖u1‖L1.a+‖u1‖Lp is small enough.Moreover the solution u(t,x)has the following large time asymptotic behavior whereO and

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Boundary Value Problems
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