1,354,727 research outputs found

    Qualitative behavior of the two-phase entropy solution of a forward-backward parabolic problem

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    We discuss some qualitative aspects of a forward-backward parabolic problem that has been introduced in [L. C. Evans and M. Portilheiro, Math. Models Methods Appl. Sci., 14 (2004), pp. 1599-1620], [C. Mascia, A. Terracina, and A. Tesei, Evolution of stable phases in forwardbackward parabolic equations, in Asymptotic Analysis and Singularities, Mathematical Society of Japan, Tokyo, 2007, pp. 451-478] and further analyzed in [C. Mascia, A. Terracina, and A. Tesei, Arch. Ration. Mech. Anal., 194 (2009), pp. 887-925]. This problem arises in models of phase transition in which two stable phases are separated by an interface. In particular, we consider here the problem of the extension in time of the solution constructed in [C. Mascia, A. Terracina, and A. Tesei, Arch. Ration. Mech. Anal., 194 (2009), pp. 887-925]. We analyze the regularity of the solution u defined in a domain R × (0, T) and give an estimate, depending on the initial datum, of the number of convex regions of the function u(·, t) for every t ε (0, T). Copyright © 2011 by SIAM

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    Game@School: Teaching STEM through mobile apps and role-based games

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    Dealing with digital native students requires new methodologies of teaching. In this work, we describe an approach and a conceptual architecture of a supporting teaching tool that takes into account two main objectives in new teaching trends: Virtual Learning Environments (VLEs) and Intelligent Pedagogical Agents (IPAs). The main idea is a VLE that in turn is a role playing game. The game structure follows a quest-based game that is deliberately designed as a system of problem-solving activities aimed at achieving objectives, to be successfully addressed in order to progress and eventually win. The emotional behavior of the IPAs has been built by conducting a study on emotions with high school students. Stemming from the study results, it has been built an Android application that uses the IPA as a standalone application to prove the efficacy of the IPA itself

    Artt. 556-557 (Bigamia)

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    Entropy formulation for forward-backward parabolic equations

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    We give a brief overview of the results obtained for forward--backward parabolic equations of cubic type. In particular we summarize an approach that has some analogies with hyperbolic conservation laws. More precisely we give a concept of entropy solution and analyze in more details admissibility conditions satisfied by an interface that separates different phases. Finally we state uniqueness and existence results that appear in literature

    A uniqueness criterion for measure-valued solutions of scalar hyperbolic conservation laws

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    We prove existence and uniqueness of Radon measure-valued solutions of the Cauchy problem for a first order scalar hyperbolic conservation law in one space dimension, the initial data being a finite superposition of Dirac masses and the flux being Lipschitz continuous, bounded and sufficiently smooth. The novelty of the paper is the introduction of a compatibility condition which, combined with standard entropy conditions, guarantees uniqueness
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