Parabolic Minkowski convolutions of solutions to parabolic boundary value problems
Parabolic Minkowski convolutions of solutions to parabolic boundary value problems
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DOI：
10.1016/j.aim.2015.10.006
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发表时间：
2016-01
影响因子：
1.7
通讯作者：
Kazuhiro Ishige;P. Salani
中科院分区：
文献类型：
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作者：
Kazuhiro Ishige;P. Salani
我们引入了一种新的卷积，它是凸分析中经典的最高卷积的一种抛物型形式。此操作允许我们比较不同区域中不同抛物线问题的解。作为主要结果的应用，我们研究了抛物型边值问题解的抛物凹性，特别是分析了具有非齐次项和非线性反应项的热方程的情形。我们还将我们的技巧应用到死核问题的研究中，得到了关于死核存在的必要条件和死核时间估计的新结果，证明了球的某些最优性。
We introduce a new kind of convolution, which is a sort of parabolic version of the classical supremal convolution of convex analysis. This operation allows us to compare solutions of different parabolic problems in different domains. As examples of applications of our main result, we study the parabolic concavity of solutions to parabolic boundary value problems, analyzing in particular the case of heat equation with an inhomogeneous term and with a nonlinear reaction term. We also apply our technique to the study of the dead core problem obtaining new results about necessary conditions for the existence of a dead core and estimates of the dead core time, proving some optimality of the ball.