The behavior of the interphase heat-transfer for the fast-igniting catalytic converter

The main purpose of this paper is to study the thermal balance equations for the gas and solid interphase heat-transfer for the fast-igniting catalytic converter of automobiles: { ∂/∂t u (t, x) = - α∂/∂x u (t, x) + av (t, x) - au (t, x) for t > 0, 0 < x < l; ∂/∂t v (t, x) = bu (t, x) - bv (t, x) + λexp (v (t, x)) for t > 0, 0 < x < l; u (t, 0) = η for t ≥ 0; u (0, x) = u₀ (x) and v (0, x) = v₀ (x) for x > 0. where u₀, v₀ are continuous functions on [0, l] with u₀ (0) = η. We establish some results concerning the existence and uniqueness of the mild solutions and classical solutions of the above differential system. The asymptotical behavior of the solution is also addressed.