Generalized solutions for the Euler-Bernoulli model with distributional forces
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We establish existence and uniqueness of generalized solutions to the initial-boundary value problem corresponding to an Euler-Bernoulli beam model from mechanics. The governing partial differential equation is of order four and involves discontinuous, and even distributional coefficients and right-hand side. The general problem is solved by application of functional analytic techniques to obtain estimates for the solutions to regularized problems. Finally, we prove coherence properties and provide a regularity analysis of the generalized solution.