Generalized solutions for the Euler–Bernoulli model with distributional forces

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.