Quenching phenomenon of singular parabolic problems with L1 initial data

We extend some previous existence results for quenching type parabolic problems involving a negative power of the unknown in the equation to the case of merely integrable initial data. We show that L1 Ω is the suitable framework to obtain the continuous dependence with respect to some norm of the initial datum; This way we answer to the question raised by several authors in the previous literature. We also show the complete quenching phenomena for such a L1-initial datum.

Is Spain Different? Innovation systems in the long-term development of the tourism sector. The IBEROSTAR case study.

Tourism is a highly competitive sector which is characterized by permanent transformation. Therefore, tourism firms depend largely on innovation to adapt themselves and compete, ensuring their survival and competitiveness. Despite research on innovation concludes that tourism firms are in most cases only moderately innovative, there are outstanding exceptions in specific fields and destinies. Spain, which is an unquestionable leader in tourism, constitutes one of them. In fact, Spanish tourism firms have shown a strong innovation capacity. They have improved and diversified their products thus meeting the requirements of a changing demand. This raises the need to properly understand how and why innovation takes place and who is involved in such a process. This paper aims to address these questions through the case study of one of the largest Spanish hospitality firms. The long history of Iberostar Group confirms that family firms and the networks they provide, along with environments that foster competition as was the case of the Spanish tourism industry, are important determinants of innovation particularly in a late-developed country.