Generalized thermoelastic models have been developed with the aim of eliminating the contradiction in the infinite velocity of heat propagation inherent in the classical dynamical coupled thermoelasticity theory. In these generalized models, the basic equations include thermal relaxation times and they are of hyperbolic type. Furthermore, Tzou established the dual-phase-lag heat conduction theo...

We propose in this paper three generalized auxiliary scalar variable (G-SAV) approaches for developing, efficient energy stable numerical schemes gradient systems. The first two G-SAV allow a range of functions the definition SAV variable, furthermore, second approach only requires total free to be bounded from below as opposed requirement that nonlinear part below. On other hand, third is unco...

Abstract We have created a functional framework for class of non-metric gradient systems. The state space is nonnegative measures, and the systems includes Forward Kolmogorov equations laws Markov jump processes on Polish spaces. This comprises definition notion solutions, method to prove existence, an archetype uniqueness result. do this by using only structure that provided directly dissipati...

We establish the following result: if the graph of a lower semicontinuous real-extendedvalued function f : Rn → R ∪ {+∞} admits a Whitney stratification (so in particular if f is a semialgebraic function), then the norm of the gradient of f at x ∈ dom f relative to the stratum containing x bounds from below all norms of Clarke subgradients of f at x. As a consequence, we obtain a Morse-Sard typ...

A few Karush-Kuhn-Tucker type of sufficient optimality conditions are given in this paper for nonsmooth continuous-time nonlinear multi-objective optimization problems in the Banach space L∞ [0, T ] of all n-dimensional vector-valued Lebesgue measurable functions which are essentially bounded, using Clarke regularity and generalized convexity. Further, we establish duality theorems for Wolfe an...

A class of multiobjective fractional programmings (MFP) are first formulated, where the involved functions are local Lipschitz and Clarke subdifferentiable. In order to deduce our main results, we give the definitions of the generalized (F,ρ) convex class about the Clarke subgradient. Under the above generalized convexity assumption, the alternative theorem is obtained, and some sufficient and ...

A new nonconvex generalized gradient is deened and some of its calculus is developed. This generalized gradient is smaller than that of Mordukhovich but still has a good calculus. This calculus includes a rule for the linear generalized gradient of positive multiples of functions, a sum rule and a chain rule.