Symmetrisers and generalised solutions for strictly hyperbolic systems with singular coefficients
Symmetrisers and generalised solutions for strictly hyperbolic systems with singular coefficients
复制标题
具有奇异系数的严格双曲系统的对称算子和广义解
DOI：
10.1002/mana.201400192
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发表时间：
2011
影响因子：
1
通讯作者：
M. Oberguggenberger
中科院分区：
文献类型：
--
作者：
Claudia Garetto;M. Oberguggenberger
本文致力于研究具有非光滑系数的严格双曲方程组和方程。在一定的平滑度以下，分布解决方案可能不存在。我们构造广义函数的Colombeau代数的广义解。推广了对称双曲型方程组的已有结果，引入了广义严格双曲性，构造了对称算子，证明了一个适当的Gårding不等式，并建立了广义解的存在性、唯一性和正则性.根据额外的正则性假设的系数，当一个经典的柯西问题的解决方案（或在分段定期的情况下的传输问题）存在，广义解被证明是与经典的解决方案（或分段经典的解决方案，满足适当的传输条件）。
This paper is devoted to strictly hyperbolic systems and equations with non‐smooth coefficients. Below a certain level of smoothness, distributional solutions may fail to exist. We construct generalised solutions in the Colombeau algebra of generalised functions. Extending earlier results on symmetric hyperbolic systems, we introduce generalised strict hyperbolicity, construct symmetrisers, prove an appropriate Gårding inequality and establish existence, uniqueness and regularity of generalised solutions. Under additional regularity assumptions on the coefficients, when a classical solution of the Cauchy problem (or of a transmission problem in the piecewise regular case) exists, the generalised solution is shown to be associated with the classical solution (or the piecewise classical solution satisfying the appropriate transmission conditions).
T 相关双曲系统的色散估计
DOI：
--
发表时间：
2008
期刊：
Rend. Sem. Mat. Univ. Pol. Torino
影响因子：
--
作者：
Jens Wirth
通讯作者：
Jens Wirth