Unique Conservative Solutions to a Variational Wave Equation
Unique Conservative Solutions to a Variational Wave Equation
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DOI：
10.1007/s00205-015-0849-y
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发表时间：
2014-11
影响因子：
2.5
通讯作者：
A. Bressan;Geng Chen;Qingtian Zhang
中科院分区：
文献类型：
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作者：
A. Bressan;Geng Chen;Qingtian Zhang
在特征分析的基础上，证明了变分波动方程守恒解的唯一性。给定一个解u（t，x），即使波速c（u）在t-x平面上仅是Hör连续的，人们仍然可以以独特的方式定义向前和向后特性。利用一组新的自变量X，Y，常数沿着特征线，我们证明了att，x，u与其它变量一起满足一个具有光滑系数的半线性系统.从这个半线性方程组解的唯一性出发，得到了具有一般初值的波动方程Cauchy问题保守解的唯一性
Relying on the analysis of characteristics, we prove the uniqueness of conservative solutions to the variational wave equation. Given a solutionu(t,x), even if the wave speedc(u) is only Hör continuous in thet–xplane, one can still define forward and backward characteristics in a unique way. Using a new set of independent variablesX,Y, constant along characteristics, we prove thatt,x,u, together with other variables, satisfy a semilinear system with smooth coefficients. From the uniqueness of the solution to this semilinear system, one obtains the uniqueness of conservative solutions to the Cauchy problem for the wave equation with general initial data