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| Initial Boundary Value Problem of an Equation fromMathematical Finance |
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Citation： |
Huashui ZHAN.Initial Boundary Value Problem of an Equation fromMathematical Finance[J].Chinese Annals of Mathematics B,2016,37(3):465~482 |
| Page view： 1505
Net amount： 980 |
Authors： |
Huashui ZHAN; |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (No.11371297) and the Science Foundation of
Xiamen University of Technology (No.XYK201448). |
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| Abstract： |
Consider the initial boundary value problem of the strong
degenerate parabolic equation
$$
\partial_{xx}u+u\partial_{y}u-\partial_{t}u =f(x,y,t,u),\quad
(x,y,t)\in Q_{T}=\Omega\times (0,T)
$$
with a homogeneous boundary condition. By introducing a new kind of
entropy solution, according to Oleinik rules, the partial boundary
condition is given to assure the well-posedness of the problem. By
the parabolic regularization method, the uniform estimate of the
gradient is obtained, and by using Kolmogoroff's theorem, the
solvability of the equation is obtained in $BV(Q_{T})$ sense. The
stability of the solutions is obtained by Kruzkov's double variables
method. |
Keywords： |
Mathematical finance, Oleinik rules, Partial boundary condition,\&Entropy solution, Kruzkov's double variables method |
Classification： |
35L65, 35L85, 35R35 |
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