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We consider the long time behavior of an infinite dimensional stochastic evolution equation with respect to a cylindrical Wiener process. New estimates on the disturbance operator related to the problem are proved using a ``variation of constants''-type formula. Such estimates, under the natural...
In this work we deal with a stability aspect of sizing optimization problems for a class of nonlinearly elastic materials, where the underlying state problem is nonlinear in both the displacements and the stresses. In  it is shown under which conditions there exists a unique solution of...
We consider an injection of incompressible viscous fluid in a curved pipe with a smooth central curve γ . The one-dimensional model is obtained via singular perturbation of the Navier—Stokes system as ɛ , the ratio between the cross-section area and the length of the pipe, tends to zero. An...
We consider a general class of problems of the minimization of convex integral functionals subject to linear constraints. Using Fenchel duality, we prove the equality of the values of the minimization problem and its associated dual problem. This equality is a variational criterion for the...
A two-dimensional model for brittle thin films is obtained from a three-dimensional fracture model for elastic material. Γ -convergence techniques are used to identify the limiting effective energy as the thickness of the sample approaches zero.
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