Piyanuch Siriwat

Mae Fah Luang University | MFU · School of Science

This paper investigates the equivalence of parabolic partial differential equations to the classical one‐dimensional heat equation using reciprocal transformations. The equations are assumed to be autonomous, and the methodology applied is similar to S. Lie's approach to solving the linearization problem of second‐order ordinary differential equati...

In this paper, we study existence and uniqueness of solutions for three-point boundary value problem for Hilfer-Hadamard sequential fractional differential equations, via standard fixed point theorems. The existence is proved by Schaefer and Krasnoselskii fixed point theorems as well and Leray-Schauder nonlinear alternative, while the existence and...

In recent years, the contamination of the aquatic environment with antibiotics, including tetracyclines, has drawn much attention. Bottom ash (BA), a residue from the biomass power plant, was used to synthesize the magnetic mesoporous silica (MMS) and was utilized as an adsorbent for tetracycline (TC) removal from aqueous solutions. The MMS was cha...

Recently, an infinitesimal approach for finding reciprocal transformations has been proposed. The method uses the group analysis approach and consists of similar steps as for finding an equivalence group of transformations. The new method provides a systematic tool for finding classes of reciprocal transformations (group of reciprocal transformatio...

The two‐dimensional two‐temperature nonstationary gas dynamics equations with the relaxation Landau–Teller equation are considered in the paper. The group analysis method is applied to the study these equations. The admitted Lie groups are found for two modifications of relaxation time. Optimal systems of one‐ and two‐dimensional subalgebras are co...

Recently, an infinitesimal approach for finding reciprocal transformations has been proposed. The method uses the group analysis approach and consists of similar steps as for finding an equivalence group of transformations. The new method provides a systematic tool for finding classes of reciprocal transformations (group of reciprocal transformatio...

Equivalence transformations play one of the important roles in continuum mechanics. These transformations reduce the original equations to simpler forms. One of the classes of nonlocal equivalence transformations is the class of reciprocal transformations. Despite the long history of applications of such transformations in continuum mechanics, ther...

In order to transform waste tea leaves into a useful/valuable material for removal of Pb²⁺ ions from wastewater, MnFe2O4/biochar was synthesized. The tea waste was pyrolyzed at 500 °C to obtain the biochar. Effects of the composition of tea leaves on the physicochemical properties of biochar were evaluated. Biochar and MnFe2O4/biochar were mainly o...

For problems with strong shock waves a modification of the Landau–Teller equation in the system of two-temperature gas dynamics is proposed. This allows for extending the admitted Lie algebra of the system by the generator of simultaneous scaling of the independent variables. On this basis a class of self-similar solutions of the one-dimensional un...

The group analysis method is applied to the plane one‐dimensional equations of two‐temperature gas dynamics. The complete classification of the equations with respect to admitted Lie group is studied. All invariant solutions are analyzed and their comparisons with the known invariant solutions of the ideal gas dynamics system are presented.

We apply the group analysis method to the plane one-dimensional equations of two-temperature gas dynamics. One class of invariant solutions is analyzed in the present paper. Stability of this class of solutions analytically as well numerically is considered.

The group analysis method is applied to the extended Green–Naghdi equations. The equations are studied in the Eulerian and Lagrangian coordinates. The complete group classification of the equations is provided. The derived Lie symmetries are used to reduce the equations to ordinary differential equations. For solving the ordinary differential equat...

A systematic application of the group analysis method for modeling fluids with internal inertia is presented. The equations studied include models such as the nonlinear one-velocity model of a bubbly fluid (with incompressible liquid phase) at small volume concentration of gas bubbles (Iordanski Zhurnal Prikladnoj Mekhaniki i Tekhnitheskoj Fiziki 3...

This paper is devoted to the detailed study one of the models, obtained in [Hematulin A, Meleshko SV, Gavrilyuk SG. Group classification of one-dimensional equations of fluids with internal inertia. Math Meth Appl Sci 2007;30:2101–20] by group analysis. The main feature of this model is that the equations describing the motion of fluids with the po...

Group classification of the three-dimensional equations describing flows of fluids with internal inertia, where the potential function W = W(ρ,ρ·), is presented. The given equations include such models as the non-linear one-velocity model of a bubbly fluid with incompressible liquid phase at small volume concentration of gas bubbles, and the disper...