| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Research Abstract |
We have studied the special solutions to the mathematical inverse problems. These solutions are called complex geometrical solutions, in short, CGO solutions. It was known that we could succeed to apply CGO solutions with linear complex phase functions to many problems. Recently new CGO solutions with nonlinear complex phase functions have been studied. But this new approach was restricted to the problems about elliptic equations as Laplace equations. So no one has understood the meaning of CGO solutions with nonlinear phase functions in general cases. In this research program we have studied new CGO solutions with nonlinear phase functions which can be applicable to general equations including hyperbolic equations. More precisely, we can derive new nonlocal Carleman estimates. By using this estimate we can study Lorentian metric and operators associated it. This is the new inverse problem related to hyperbolic equations.
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