Erratum to: Symmetries and stability of motions in the Newtonian and the Hookean potentials (Theor. Appl. Mech. 49(1) (2022), 61--69) DOI: https://doi.org/10.2298/TAM220213005C
Christian Carimalo
Available online 28 February 2025

Abstract

Mathematics Subject Classification

Keywords

DOI
https://doi.org/10.2298/TAM231221002E

Viscous dissipation effects in a vertical annulus filled with fluid-saturated porous medium
Eduard Marušić-Paloka and Igor Pažanin
Available online 05 June 2025

Abstract
The investigation of heat transfer within porous medium has attracted considerable interest because of its growing practical importance. The present paper is devoted to the study of a steady-state non-isothermal fluid flow through a vertical cylindrical annulus filled with sparsely packed porous medium. The governing system is given by the Darcy-Brinkman-Boussinesq model where the heat equation includes the viscous dissipation term. The side walls are maintained at uniform temperatures, while the flow is driven by the axial pressure gradient. Introducing the thickness of the annular region as the small parameter of the problem, the goal is to derive the approximation of the flow via asymptotic analysis. Although the governing problem is coupled and nonlinear, the asymptotic solution is proposed in the explicit form and that represents our main contribution. As such, it clearly displays the effects of porous structure and viscous dissipation on the temperature and velocity distribution. Due to the viscous dissipation, we observe the increase in the heat generation leading to a raise in the temperature and velocity profile within the annulus. Moreover, it is deduced that reducing the thickness of the annular region may be employed to strengthen the seepage velocity of the working fluid.

Mathematics Subject Classification
35B40, 35Q35, 76S05

Keywords
cylindrical annulus, viscous dissipation, porous medium, asymptotic analysis

DOI
https://doi.org/10.2298/TAM250311009M

Blow-up phenomena for a damped wave equation with logarithmic source term and variable-exponents
Mohammed Y. Trigui and Mohamed Saadaoui
Available online 03 November 2025

Abstract
This paper investigates the wave equation with variable-exponent nonlinearity and logarithmic source term, given by the following: where $a$ and $b$ are positive constants, and the functions $m(·)$ and $p(·)$ satisfy certain required conditions. Using the energy method and several inequality techniques, we establish a finite-time global nonexistence result for specific solutions with positive initial energy, under appropriate conditions. This type of equation has significant applications in various fields, including fluid dynamics, electrorheological fluids, quantum mechanics, nuclear physics, optics, and geophysics.

Mathematics Subject Classification
35L05, 35L20, 35L70, 35B40, 35B44

Keywords
wave equation, variable exponent, logarithmic source, blow-up

DOI
https://doi.org/10.2298/TAM250112018T

On global existence of weak solutions for compressible self-gravitating fluids with unbounded domains
Jan Muhammad
Available online 08 December 2025

Abstract
This paper examines to the global existence of weak solutions for compressible self-gravitating fluids in three-dimensional unbounded domain with a compact Lipschitz boundary, assuming a total finite fluid mass. We prove that there exists a globally defined weak solution that satisfies the energy inequality in differential form.

Mathematics Subject Classification
35Q35; 76E19

Keywords
weak solutions, energy inequality, compressible self-gravitating fluid, unbounded domain

DOI
https://doi.org/10.2298/TAM250226019M

Well posedness and stabilisation for a flexible mechanical system under distributed delay
Billal Lekdim
Available online 02 February 2026

Abstract
In this paper, we investigate the boundary control of flexible mechanical systems characterized by bending deformation, torsion deformation, and distributed delay. We establish the existence of solutions using the Faedo-Galerkin approach along with energy estimates. Under appropriate assumptions on the delay weight and the proposed control, we demonstrate the exponential stability of the solution via the Lyapunov method.

Mathematics Subject Classification
35B35, 35B40, 93D23; 35R09

Keywords
exponential stability, well-posedness, boundary control, Faedo-Galerkin, Lyapunov method

DOI
https://doi.org/10.2298/TAM250425001L

Optimal synthesis for an intermediate vehicle model with state constraints
E. V. Malykh and O. Yu. Cherkasov
Available online 02 February 2026

Abstract
The problem of optimal thrust programming for an intermediate vehicle model is considered. The motion occurs in a vertical plane under a uniform gravitational field, quadratic resistance friction, and thrust force. The control variables are the angle of attack and the thrust force. Phase constraints are imposed on the trajectory inclination angle. It is assumed that the total fuel consumption for thrust control is negligible compared to the vehicle mass, the fuel mass variation does not affect the center of mass dynamics, and a change of the lifting force does not affect the drag force. The region in the space of initial variables for which the problem is solvable is determined, and an optimal synthesis is constructed. It is established that within this domain, the thrust can be maximum, intermediate, or zero. The number and sequence of trajectory arcs with corresponding thrust values and the number of exits to state constrains are determined.

Mathematics Subject Classification
49N35, 49N90, 37N40

Keywords
singular control, two-dimensional Goddard problem, brachistochrone, quadratic drag, optimal synthesis, state constraints

DOI
https://doi.org/10.2298/TAM250603002M