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Weighted Inertia-Dissipation-Energy Functionals for Semilinear Equations

Matthias Liero;  Ulisse Stefanelli — 2013

Bollettino dell'Unione Matematica Italiana

We address a global-in-time variational approach to semilinear PDEs of either parabolic or hyperbolic type by means of the so-called Weighted Inertia-Dissipation-Energy (WIDE) functional. In particular, minimizers of the WIDE functional are proved to converge, up to subsequences, to weak solutions of the limiting PDE. This entails the possibility of reformulating the limiting differential problem in terms of convex minimization. The WIDE formalism can be used in order to discuss parameters asymptotics...

Rate independent Kurzweil processes

Pavel Krejčí;  Matthias Liero — 2009

Applications of Mathematics

The Kurzweil integral technique is applied to a class of rate independent processes with convex energy and discontinuous inputs. We prove existence, uniqueness, and continuous data dependence of solutions in B V spaces. It is shown that in the context of elastoplasticity, the Kurzweil solutions coincide with natural limits of viscous regularizations when the viscosity coefficient tends to zero. The discontinuities produce an additional positive dissipation term, which is not homogeneous of degree...

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