Research Of The Transport Equation For A Growing Bacterial Populations

This article studies the transport equation of the growing bacterial populations with generalized boundary conditions in1 X space, and the main results have three points. First, it is proved that the transport operatorpA?, generates irreducible positive 0C semigroup; Second, it discusses the spectral analysis of the transport operator,, pA? which it proves that the transport operator has the existence of the isolate eigenvalues with finite algebraic multiplicity, and the spectrum of the transport operator consists of at most finitely isolate eigenvalues with finite algebraic multiplicities in the region of right half plane, and the existence of the dominant eigenvalue in 2X space;Third, the essential types of the semigroup is generated by the streaming operator is consistent with the essential types of the semigroup is generated by the transport operator, it is to obtain that the asymptotic behavior of the transport equation's solution, and so on. The difficulties of it lie in:(1) it calculated the irreducibility of the positive 0C semigroup;(2) it is to calculate that the monotonicity of the spectral radius for the assist operator, etc;(3) it is to prove that the spectrum of the transport operator consists of only finitely isolate eigenvalues with finite algebraic multiplicities in the region of right half plane;(4) it proves the existence of the dominant eigenvalue for the transport operator;(5) it is to calculate that the weakly compactness of the product for the semigroup is generated by the streaming operator and the several operators;(6) it is to discuss that the asymptotic behavior of the transport equation's solution, and so on.