Abstract
In this paper, we study a mixed problem with integral boundary conditions for a high order partial differential equation of mixed type. We prove the existence and uniqueness of the solution. The proof is based on energy inequality, and on the density of the range of the operator generated by the considered problem.
Highlights
PARTIAL DIFFERENTIAL EQUATIONUniversité Mentouri Constantine Institut de Mathematiques 25000 Constantine, Algeria (Received April, 2000; Revised March, 2002)
In the rectangle, we consider the equation (1)where is bounded for i that andTo equation (1) we add the initial conditions, and has bounded partial derivatives such, for (2)the boundary conditions for (3) for (4)and integral condition (5)where and are known functions which satisfy the compatibility conditions given in equations (3)-(5).Integral boundary conditions for evolution problems have various applications in chemical engineering, thermoelasticity, underground water flow and population dynamics; see for example Choi and Chan [6], Ewing and Lin [7], Shi [12], and Shi and Shillor [13]
And has bounded partial derivatives such, for the boundary conditions for and integral condition where and are known functions which satisfy the compatibility conditions given in equations (3)-(5)
Summary
Université Mentouri Constantine Institut de Mathematiques 25000 Constantine, Algeria (Received April, 2000; Revised March, 2002).
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