In this paper we establish new forward and backward versions of Ekeland’s variational principle for the class of strictly-decreasing forward(resp. backward-) lower-semicontinuou functionals in pseudo-quasimetric spaces. We do not require that the space under consideration either is complete or enjoys the limit uniqueness property due to the fact that the collections of forward and backward limi...

The variational principle of barotropic Eulerian fluid dynamics is known to be quite cumbersome containing as much as eleven independent functions. This is much more than the the four functions (density and velocity) appearing in the Eulerian equations of motion. This fact may have discouraged applications of the variational method. In this paper a four function Eulerian variational principle i...

The present study is concerned with the variational principle and plane wave propagation in double porous thermoelastic infinite medium. Lord-Shulman theory [2] of thermoelasticity with one relaxation time has been used to investigate the problem. It is found that for two dimensional model, there exists four coupled longitudinal waves namely longitudinal wave (P), longitudinal thermal wave (T),...

We establish the variational principle of Kolmogorov-PetrovskyPiskunov (KPP) front speeds in a one dimensional random drift which is a mean zero stationary ergodic process with mixing property and local Lipschitz continuity. To prove the variational principle, we use the path integral representation of solutions, hitting time and large deviation estimates of the associated stochastic flows. The...

This paper adopts Rotem and Shinnar?s modification of the Rabinowitsch fluid model for one-dimensional non-Newtonian lubrication problem, a variational principle is established by semi-inverse method, generalized Reynolds-type equation obtained. article opens new avenue establishment complex problems.

h this paper, we use the auxiliary principle technique to suggest a new &ass of predictor-corrector algorithms for solving generalized variational inequalities. The convergence of the proposed method only requires the partially relaxed strongly monotonicity of the operator, which is weaker than co-coercivity. As special cases, we obtain a number of known and new results for solving va,rious cla...

The multiscale coarse-graining (MS-CG) method [S. Izvekov and G. A. Voth, J. Phys. Chem. B 109, 2469 (2005); J. Chem. Phys. 123, 134105 (2005)] employs a variational principle to determine an interaction potential for a CG model from simulations of an atomically detailed model of the same system. The companion paper proved that, if no restrictions regarding the form of the CG interaction potent...

The fractal derivative is adopted to describe the non-linear fractional wave equation in a space. A variational principle successfully established by semi-inverse method. two-scale method and He?s exp-function are used solve equation, good result obtained.

As we will see during this talk, the Bayesian and information-theoretic views of variational inference provide complementary and mutually beneficial perspectives to the same problems with two different languages. More specifically, based on the paper by Honkela and Valpola [4], we will provide an interpretation of variational inference based on the MDL principle as a theoretical framework for m...

We introduce a variational principle suitable for the computational modeling of crystalline materials. We consider a class of materials that are described by non-quasiconvex variational integrals. We are further focused on equlibria of such materials that have non-attainment structure, i.e., Dirichlet boundary conditions prohibit these variational integrals from attaining their infima. Conseque...