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Existence and uniqueness of a generalized solution to the one-dimensional flow and thermal explosion micropolar reactive real gas model

In this work, we consider the model of one- dimensional flow and thermal explosion of reactive micropolar gas, taking into account the equation of state of real gas given by P = Rρ^pθ, (1) where P is the pressure, ρ is the mass density, θ is the absolute temperature, and R > 0 is a constant. Exponent p ≥ 1 is called pressure exponent. First, the corresponding boundary-initial value problem with homogeneous boundary conditions in mass Lagrangian coordinates is derived, then the notion of a generalized solution is defined and its existence and uniqueness are considered. Namely, it was first proved that the described problem has a solution locally in time [4]. To prove this result, a constructive technique involving Faedo- Galerkin approximations was used. It was also shown that the problem admits at most one generalized solution. Finally, using the theorems on local existence and uniqueness, it is shown that the solution can be extended to an interval of arbitrary finite length. The problem is also solved numerically, using the same construction as in the proof of the theorem on local existence.

micropolar fluid ; real gas ; reactive fluid

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