| 詹华税.拟线性退化抛物方程Cauchy问题的解[J].数学年刊A辑,2012,33(4):449~460 |
| 拟线性退化抛物方程Cauchy问题的解 |
| Solutions to the Cauchy Problem of a Quasilinear Degenerate Parabolic Equation |
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| DOI： |
| 中文关键词: 退化抛物方程 熵解 Cauchy问题 爆破 强解 |
| 英文关键词:Degenerate parabolic equation, Entropy solution, Cauchy problem,
Blow-up, Strong solution |
| 基金项目:福建省自然科学基金(No.2009J01009);集美大学潘金龙科学基金(No.ZC2010019)资助的项目 |
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| 中文摘要: |
| 对来自金融数学领域的方程xxu+uyu-tu=c（x,y,t,u）,（x,y,t）∈QT=R2×[0,T)的Cauchy问题,给出了一种新的熵解的定义,得到了其适定性结果.可以证明所得到的解还是强解,即方程中所出现的各阶偏导数几乎处处连续.最后讨论了解的爆破性质以及与解的间断点相关的几何性质. |
| 英文摘要: |
| The paper gives a new definition of the entropy solution to the
Cauchy problem of the following equation coming from finance mathematics:
\partial_{xx}u+u\partial_{y}u-\partial_{t}u=c(x,y,t,u), \quad (x,y,t)\in Q_T=
\mathbb{R}^{2}\times[0,T)
and gets its well-posedness. Moreover, it can be proved that this
solution is a strong solution, which means all the partial
derivatives emerging in the equation are almost everywhere
continuous in $Q_{T}$. At the same time, the blow-up phenomena of
the solutions and the geometrical properties of the jump points of
the solutions are discussed. |
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