We study a restricted weak lower semicontinuity property, which we call the (PS)-weak lower semicontinuity, for a smooth integral functional on the Sobolev space along all weakly convergent Palais-Smale sequences of the functional. By the Ekeland variational principle, the (PS)-weak lower semicontinuity is sufficient for the existence of minimizers under the usual coercivity assumption. In gene...

In order to characterize the complexity of a system with zero entropy we introduce the notions of scaled topological and metric entropies. We allow asymptotic rates of the general form e determined by an arbitrary monotonically increasing “scaling” sequence a(n). This covers the standard case of exponential scale corresponding to a(n) = n as well as the cases of zero and infinite entropy. We de...

Abstract. We use a new variational method—based on the theory of anti-selfdual Lagrangians developed in [2] and [3]—to establish the existence of solutions of convex Hamiltonian systems that connect two given Lagrangian submanifolds in R . We also consider the case where the Hamiltonian is only semi-convex. A variational principle is also used to establish existence for the corresponding Cauchy...

A recently developed variational principle of virtual dissipation along with a new approach to the thermodynamics of open systems is applied to coupled mass and heat transfer in a porous solid containing a fluid. General differential field equations are derived directly from the variational principle. A general energy flux theorem is formulated. Vapor-liquid phase transition and capillary conde...

Like mechanics and electrodynamics, the fundamental laws of the thermodynamics of dissipative processes can be compressed into a variational principle. This variational principle both in its differential (local) and in integral (global) forms was formulated by Gyarmati helped by the present author in 1965. This principle was applied to several fields of irreversible processes: first of all, his...

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...

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...

The present paper is on the existence and behaviour of solutions for a class semilinear parabolic equations, defined bounded smooth domain assuming nonlinearity asymptotically linear at infinity. behavior when initial data varies in phase space analyzed. Global are obtained, which may be or blow-up infinite time (grow-up). main tools comparison principle variational methods. In particular, Neha...

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...