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Yevgeniia Yevgenieva

Publications and source records attributed to Yevgeniia Yevgenieva.

10 recordsLinked to original sources
arXiv2026

Exponential Decay for a Boundary-Controlled Nonlinear Parabolic Reactor Model

We study an axial dispersion tubular reactor model governed by a nonlinear parabolic equation with Robin-type boundary conditions and boundary feedback control. We derive sufficient conditions for the exponential stability of the steady-state solution of the closed-loop system and provide an explicit estimate of the decay rate. In addition, numerical simulations are presented to illustrate the sharpness of the obtained decay rate for different choices of the feedback gain parameter.

math.AP↗
arXiv2026

Regularity for Doubly Nonlinear Equations in the Mixed Regime

We study the local Hölder continuity of nonnegative solutions to doubly nonlinear equations by introducing a new technique that allows us to treat the cases where the equation is both singular and degenerate, up to specific Barenblatt numbers. Our argument relies on a new integral $L^1$-$L^1$ Harnack estimate, of independent interest.

math.AP↗
arXiv2025

On the continuity of solutions to the anisotropic $N$-Laplacian with $L^1$ lower order term

We establish the continuity of bounded solutions to the anisotropic elliptic equation $$-\sum\limits_{i=1}^N\Big(|u_{x_i}|^{p_i-2} u_{x_i}\Big)_{x_i}=f(x),\quad x\in Ω,\quad f(x)\in L^1(Ω)$$ under the conditions $$\min\limits_{1\leqslant i\leqslant N} p_i >1,\quad \sum\limits_{i=1}^N \frac{1}{p_i}=1$$ and $$\lim\limits_{ρ\rightarrow 0}\,\sup\limits_{x\in Ω}\int\limits^ρ_0\Big(\int\limits_{B_r(x)}|f(y)|\,dy\Big)^{\frac{1}{N-1}}\frac{dr}{r}=0.$$ In the standard case $p_1=...=p_N=N$, these conditions recover the known results for the $N$-Laplacian.

math.AP↗
arXiv2025

Stability and decay rate estimates for a nonlinear dispersed flow reactor model with boundary control

We investigate a nonlinear parabolic partial differential equation whose boundary conditions contain a single control input. This model describes a chemical reaction of the type ``$A \to $ product'', occurring in a dispersed flow tubular reactor. The existence and uniqueness of solutions to the nonlinear Cauchy problem under consideration are established by applying the theory of strongly continuous semigroups of operators. We also prove the stability of the equilibrium of the closed-loop system with a proposed feedback law. Additionally, using Lyapunov's direct method, we evaluate the exponential decay rate of the solutions.

math.AP↗
arXiv2024

Partial Stabilization of an Orbiting Satellite Model with a Flexible Attachment

We consider a mathematical model of an orbiting satellite, comprising a rigid carrier body and a flexible boom, operating under the influence of gravity gradient torque. This model is represented by a nonlinear control system, which includes ordinary differential equations governing the carrier body's angular velocity and attitude quaternion, coupled with the Euler-Bernoulli equations that describe the vibration of the flexible component. We propose an explicit feedback design aimed at guaranteeing the partial stability of the closed-loop system in an appropriate Hilbert space.

math.OC↗
arXiv2024

On the Controllability of an Orbiting Satellite Model with Electromagnetic-only Actuation

This paper presents sufficient conditions for small-time local controllability of a control-affine system that describes the rotational motion of a satellite in a circular orbit. The satellite is modeled as a rigid body subject to electromagnetic actuation. We focus on the underactuated scenario where the control torque is generated solely by magnetorquers. The main contributions of this work include proving small-time local controllability around the relative equilibrium under some natural assumptions on the mass distribution of the rigid body. This result is based on the Lie algebra rank condition and Sussmann's controllability condition. Furthermore, it is shown that the linearized system is not controllable in a neighborhood of the considered equilibrium.

math.OC↗
arXiv2023

Periodic optimal control of a plug flow reactor model with an isoperimetric constraint

We study a class of nonlinear hyperbolic partial differential equations with boundary control. This class describes chemical reactions of the type ``$A \to$ product'' carried out in a plug flow reactor (PFR) in the presence of an inert component. An isoperimetric optimal control problem with periodic boundary conditions and input constraints is formulated for the considered mathematical model in order to maximize the mean amount of product over the period. For the single-input system, the optimality of a bang-bang control strategy is proved in the class of bounded measurable inputs. The case of controlled flow rate input is also analyzed by exploiting the method of characteristics. A case study is performed to illustrate the performance of the reaction model under different control strategies.

math.OC↗
arXiv2023

Harnack's inequality for degenerate double phase parabolic equations under the non-logarithmic Zhikov's condition

We prove Harnack's type inequalities for bounded non-negative solutions of degenerate parabolic equations with $(p,q)$ growth $$ u_{t}-{\rm div}\left(\mid \nabla u \mid^{p-2}\nabla u + a(x,t) \mid \nabla u \mid^{q-2}\nabla u \right)=0,\quad a(x,t) \geq 0 , $$ under the generalized non-logarithmic Zhikovs conditions $$ \mid a(x,t)-a(y,τ)\mid \leqslant Aμ(r) r^{q-p},\quad (x,t),(y,τ)\in Q_{r,r}(x_{0},t_{0}),$$ $$\lim\limits_{r\rightarrow 0}μ(r) r^{q-p}=0,\quad \lim\limits_{r\rightarrow 0}μ(r)=+\infty,\quad \int\limits_{0} μ^{-β}(r)\frac{dr}{r} =+\infty,$$ with some $β>0$.

math.AP↗