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We address the existence of a weak notion of solution, referred to as \u201centropic,\u201d where the temperature equation is formulated with the aid of an entropy inequality, and of a total energy inequality. This solvability concept reflects the basic principles of thermomechanics, as well as the thermodynamical consistency of the model. It allows us to obtain global-in-time existence theorems without imposing any restriction on the size of the initial data. We prove our results by passing to the limit in a time-discretization scheme, carefully tailored to the nonlinear features of the PDE system (with its entropic formulation) and of the a priori estimates performed on it. Our time-discrete analysis could be useful toward the numerical study of this model.<\/jats:p>","DOI":"10.1137\/140960803","type":"journal-article","created":{"date-parts":[[2015,7,3]],"date-time":"2015-07-03T11:31:59Z","timestamp":1435923119000},"page":"2519-2586","source":"Crossref","is-referenced-by-count":28,"title":["``Entropic\u201d Solutions to a Thermodynamically Consistent PDE System for Phase Transitions and Damage"],"prefix":"10.1137","volume":"47","author":[{"given":"Elisabetta","family":"Rocca","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Riccarda","family":"Rossi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,7,2]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-009-0806-4"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2010.10.037"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/0322035"},{"key":"atypb4","series-title":"Lecture Notes in Phys","first-page":"207","volume-title":"PDEs and Continuum Models of Phase Transitions (Nice","author":"Ball J. 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