Findings reveal a priori estimates for solution norms in a boundary value problem with variable coefficients, indicating implications for thermal diffusion modeling.
The global solvability and local uniqueness of a new boundary value problem for a stationary thermal diffusion model with variable coefficients, taking into account the Soret effect, are proven. A priori estimates of the norms of the main components of the solution are derived and analyzed, depending on the norms of the problem data and the leading coefficients of the model. A special dependence of the solution on the modulus of the Soret coefficient is established.
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Alekseev et al. (2025) studied this question.
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