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In this paper we use convex analysis and variational inequality methods to establish an existence result for a model of infinitesimal rate-independent gradient plasticity with kinematic hardening and plastic spin, in which the local…
Materials under complex loading develop large strains and often transition via an elastic instability, as observed in both simple and complex systems. Here, we present Si I under large strain in terms of Lagrangian strain by an…
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We show existence of solutions for the equations of static atomistic nonlinear elasticity theory on a bounded domain with prescribed boundary values. We also show their convergence to the solutions of continuum nonlinear elasticity theory,…
We investigate a one-dimensional nonlinear wave system which arises from a variational principle modeling a type of cholesteric liquid crystals. The problem treated here is the Cauchy problem for the same wave speed case with initial data…
In this paper, we investigate an ill-posed Cauchy problem involving a stochastic parabolic equation. We first establish a Carleman estimate for this equation. Leveraging this estimate, we derive the conditional stability and convergence…
In this paper, we establish the existence of a 1-parameter family of spatially inhomogeneous radially symmetric classical self-similar solutions to a Cauchy problem for a semi-linear parabolic PDE with non-Lipschitz nonlinearity and trivial…
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