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In this paper, we consider an Euler-Bernoulli beam equation with time-varyinginternal fluid. We assume that the fluid is moving with non-constant velocityand dynamical boundary conditions are satisfied. We prove the existence anduniqueness of global solution under suitable assumptions on the tension of beamand on the parameters of the problem. Afterwards, we establish the exponentialstability of the solution by introducing a suitable Lyapunov functional.

zeitschrift für angewandte mathematik und physik

Well-posedness and exponential decay for the Euler-Bernoulli beam  conveying fluid equation with non-constant velocity and dynamical boundary  conditions