Stability of boundary-value problems for third-order partial differential equations

Abstract

We consider a boundary-value problem for the third-order partial differential equation $$\displaylines{ \frac{d^3u(t)}{dt^3}+Au(t)=f(t),\quad 0<t<1, \cr u(0)=\varphi,\quad u(1)=\psi,\quad u'(1)=\xi }$$ in a Hilbert space H with a self-adjoint positive definite operator A. Using the operator approach, we establish stability estimates for the solution of the boundary value problem. We study three types of boundary value problems and obtain stability estimates for the solution of these problems.

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