AbstractThe model equations of the catalytic fixed‐bed reactor often possess solutions in the form of travelling wave fronts similar to the well‐known case of Fisher's equation. The mathematical investigation of these waves requires searching for solutions of singular boundary value problems in the phase plane or in the three‐dimensional phase space. In this paper necesary and sufficient conditions are derived which are to be satisfied by the model parameters and the propagation velocity of the wave front if wave solutions exist. Moreover, sufficient conditions for the asymptotic stability of these solutions are proved where the perturbations are supposed to belong to a certain weightedL2‐space. Finally, the connection between the initial distribution of the state variable and the velocity of the wave is di
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