On an Inverse Problem for the Hyperbolic Equation
نویسندگان
چکیده
The paper considers the inverse problem of determining unknown coefficient on righthand side hyperbolic equation. An additional condition for finding coefficient, which depends variable time, is given in integral form. Theorems uniqueness, stability, and existence solution have been proved.
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برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.
15 صفحه اولProperty C and an Inverse Problem for a Hyperbolic Equation
Let (* ) u,, du + q(x, t) u = 0 in D x [0, T], where D c R3 is a bounded domain with a smooth boundary dD, T> d, d: =diam D, q(x, I) E C( [O, 2’1, L”(D)). Suppose that for every (**) ~I,+~=f(x, l)EC’(dDx [0, T]), the value u*,;,:= h(s, t) is known, where N is the outer normal to dD, u solves (* ) and ( ** ) and satisfies the initial conditions u = U, = 0 at I = 0. Then q(x, I) is uniquely deter...
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ژورنال
عنوان ژورنال: Journal of Mathematical Sciences
سال: 2022
ISSN: ['1072-3374', '1573-8795']
DOI: https://doi.org/10.1007/s10958-022-06187-y