Heat-like and wave-like lifespan estimates for solutions of semilinear damped wave equations via a Kato's type lemma

In this work we consider several semilinear damped wave equations with “subcritical” nonlinearities, focusing on studying lifespan estimates for energy solutions. Our main concern is on equations with scale-invariant damping and mass. By imposing different assumptions on the initial data, we prove lifespan estimates from above, distinguishing between “wave-like” and “heat-like” behaviours. Furthermore, we conjecture logarithmic improvements for the estimates on the “transition surfaces” separating the two behaviours. As a direct consequence, we reorganize the blow-up results and lifespan estimates for the massless case, and we obtain in particular improved lifespan estimates for the one dimensional case, compared to the known results. We also study semilinear wave equations with scattering damping and negative mass term, finding that if the decay rate of the mass term equals to 2, the lifespan estimate coincides with the one in a special case of scale-invariant damped equation. The main tool employed in the proof is a Kato's type lemma, established by iteration argument

The genotoxic air pollutant 3-nitrobenzanthrone and its reactive metabolite N-hydroxy-3-aminobenzanthrone lack initiating and complete carcinogenic activity in NMRI mouse skin

3-Nitrobenzanthrone (3-NBA), a genotoxic mutagen found in diesel exhaust and ambient air pollution and its active metabolite N-hydroxy-3-aminobenzanthrone (N-OH-3-ABA) were tested for initiating and complete carcinogenic activity in the NMRI mouse skin carcinogenesis model. Both compounds were found to be inactive as either tumour initiators or complete carcinogens in mouse skin over a dose range of 25-400 nmol. Topical application of 3-NBA and N-OH-3-ABA produced DNA adduct patterns in epidermis, detected by P-32-postlabelling, similar to those found previously in other organs of rats and mice. 24 h after a single treatment of 100 nmol DNA adduct levels produced by 3-NBA (18 +/- 4 adducts/10(8) nucleotides) were 6 times lower than those by 7,12-dimethylbenz[a]anthracene (DMBA; 114 +/- 37 adducts/10(8) nucleotides). In contrast, identical treatment with N-OH-3-ABA resulted in adduct levels in the same range as with DMBA (136 +/- 25 adducts/10(8) nucleotides), indicating that initial DNA adduct levels do not parallel tumour initiating activity. When compounds were tested for tumour initiating activity by a single treatment followed by twice-weekly applications of TPA. DNA adducts formed by DMBA, but not by 3-NBA or N-OH-3-ABA, were still detectable 40 weeks after treatment. When tested for activity as complete carcinogens by twice-weekly topical application, 3-NBA and N-OH-3-ABA produced identical DNA adduct profiles in mouse skin, with adducts still detectable after 40 weeks. Only 3-NBA produced detectable adducts in other organs. (C) 2009 Elsevier Ireland Ltd. All rights reserved