<f>L1</f> stability estimate for a one-dimensional Boltzmann equation with inelastic collisions

In this paper, we study the <f>L1</f> stability of a one-dimensional Boltzmann equation on the line with inelastic collisions in Rend. Sem. Mat. Fis. Milano 67 (1997) 169–179. Under the suitable assumptions on the initial data, we construct a nonlinear functional <f>H(t)</f> which measures <f>L1</f> distance between two mild solutions, and is nonincreasing in time <f>t</f>. Using the time-decay estimate of <f>H(t)</f>, we show that mild solutions are <f>L1</f>-stable:||f(· ,· ,t)−f¯(· ,· ,t)||L1(R2)&les;G||f0(· ,·)−f¯0(· ,·)||L1(R2),where <f>G</f> is a positive constant independent of time <f>t</f>, <f>f</f> and <f>f¯</f> are mild solutions corresponding to initial data <f>f0</f> and <f>f¯0</f> in <f>L1(R2)∩L+∞(R2)</f>, respectively. [Copyright &y& Elsevier]