This paper presents a generalization for systems of partial differential equations of Gronwall's classical integral inequality for ordinary differential equations. The proof is by reducing the vector integral inequality to a vector partial differential inequality and then using a vector generalization of Riemann's method to obtain the final inequality. The final inequality involves a matrix fun...

This paper is devoted to one-dimensional interpolation Gagliardo-Nirenberg-Sobolev inequalities. We study how various notions of duality, transport and monotonicity of functionals along flows defined by some nonlinear diffusion equations apply. We start by reducing the inequality to a much simpler dual variational problem using mass transportation theory. Our second main result is devoted to th...

In the paper we investigate solvability of nonlinear optimal Thermal and Diffusion processes control problems defined by semi-linear parabolic equations when the source function nonlinearly depends on the controlling parameters, and nonlinear integral criterion of quality is minimized. We obtained the sufficient conditions of uniqueness of the solution of the boundary value problem and the adjo...

We prove existence of positive solutions to a nonlinear fractional boundary value problem. Then, under some mild assumptions on the nonlinear term, we obtain a smart generalization of Lyapunov’s inequality. The new results are illustrated through examples.

CONTENTS Introduction. 0. Pseudodifferential operators and linear PDE. §0.1 The Fourier integral representation and symbol classes §0.2 Schwartz kernels of pseudodifferential operators §0.3 Adjoints and products §0.4 Elliptic operators and parametrices §0.5 L 2 estimates §0.6 Gårding's inequality §0.7 The sharp Gårding inequality §0.8 Hyperbolic evolution equations §0.9 Egorov's theorem §0.10 M...

The well-known Baum-Eagon inequality I31 provides an effective iterative scheme for finding a local maximum for homogeneous polynomials with positive coefticients over a domain of probability values. However, in many applications we are interested in maximizing a general rational function. We extend the Baum-Eagon inequality to rational functions. We briefly describe some of the applications of...

It is known that vector variational inequality models arises from vector optimization and vector traac equilibria. In this paper, existence results of a solution for a generalized pre-vector variational inequality and a generalized pre-quasi-vector variational inequality are established. The main condition used is that the underlying vector-valued function is assumed to be cone-quasi-convex. Th...

This paper presents a new controller for speed control problem of the BLDC motors. The nonlinear model of the motor is approximated by implementation of fuzzy rules. The uncertainties are considered in the fuzzy system. Using this model and linear matrix inequality (LMI) optimization, a robust controller for purpose of speed control of the motor has been designed and applied to it. The effectiv...

This paper argues that the conventional approach of data averaging is problematic for exploring the growth–inequality nexus. It introduces the polynomial inverse lag (PIL) framework so that the impacts of inequality on investment, education, and ultimately on growth can be measured at precisely defined time lags. Combining PIL with simultaneous systems of equations, we analyze the growth–inequa...