Solvability of the initial boundary value problem for the continuum transfer equation in the class of summable functions in a network-like domain

Title	Solvability of the initial boundary value problem for the continuum transfer equation in the class of summable functions in a network-like domain
Authors	I. V. Guselnikova¹ ¹Peter the Great St.Petersburg Polytechnic University
Annotation	A method for analyzing evolutionary models of transport processes in network-like domains is presented. The study is conducted using the Dirichlet problem for a parabolic equation in a weak formulation, where the differential equation itself is replaced by an integral identity. The proposed method is applicable with slight modifications in the case of elliptic, hyperbolic, and other problems for vector functions. An example of the latter is the linearized Navier-Stokes system, which is widely used in the description of network-like hydrodynamic processes.
Keywords	network-like domain, evolutionary model of the transfer process, Navier-Stokes system, solvability of initial boundary value problems.
Citation	Guselnikova I. V. ''Solvability of the initial boundary value problem for the continuum transfer equation in the class of summable functions in a network-like domain'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 29-31, 2025). Saransk: SVMO Publ, 2025. - pp. 85-90. Available at: https://conf.svmo.ru/files/2025/papers/paper17.pdf. - Date of access: 30.08.2025.