Local existence for viscous reactive micropolar real gas flow and thermal explosion with homogeneous boundary conditions

Uniqueness of a Generalized Solution for a One-Dimensional Thermal Explosion Model of a Compressible Micropolar Real Gas

“…In this work, the problem of the thermal explosion of a real gas is extended to the micropolar case, and the corresponding model is governed by ( 1)- (8). For this problem, the local and global existence of a generalized solution has been proved so far [7,41], and the uniqueness of the generalized solution is proved in this work.…”

“…Let us mention that in [7] it is shown that the initial-boundary value problem ( 1)-( 8) has a generalized solution locally in time if the following holds for the initial functions:…”

“…Theorem 1 (On the local existence of the generalized solution [7]). Let the functions ρ 0 , v 0 , ω 0 , θ 0 , z 0 satisfy the conditions ( 34)- (35).…”

“…for (x, t) ∈]0, 1[×]0, T[. The system is coupled with the following initial conditions ρ(x, 0) = ρ 0 (x), v(x, 0) = v 0 (x), ω(x, 0) = ω 0 (x), θ(x, 0) = θ 0 (x), z(x, 0) = z 0 (x), (7) for x ∈ [0, 1], and the following homogeneous boundary conditions v(0, t) = v(1, t) = 0, ω(0, t) = ω(1, t) = 0,…”

“…where A is a quasi-linear elliptic spatial differential operator, where the quasi-linearity is characterized by linearity in the highest-order derivatives, more precisely, in the secondorder derivatives. This form of the problem is advantageous since some general methods for its solution are known, such as the Faedo-Galerkin projection onto finite-dimensional subspaces (see [6]), which was used to prove the existence of this problem in [7].…”