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Abstract: This paper is concerned with the spreading speeds and traveling wave solutions of a nonlocal dispersal equation with degenerate monostable nonlinearity. We first prove that the traveling wave solution with critical minimal speed decays exponentially as , while other traveling wave solutions with do not decay exponentially as . Then the monotonicity and uniqueness (up to translation) of traveling wave solution with critical minimal speed is established. Finally, we prove that the critical minimal wave speed coincides with the asymptotic speed of spread. [Copyright &y& Elsevier]

Abstract: This paper studies the existence, uniqueness and asymptotic behavior of the solution for a half-space linearized stationary Boltzmann equation with an external force term, in the case of a specified incoming distribution at the boundary and a given mass flux. Without the external force, the solution of the stationary Boltzmann equation has been proved to tend toward a constant state, which is independent of the space variable. Due to the presence of the external force, we show that the solution tends to some function which depends on the space variable. [Copyright &y& Elsevier]