An inverse “source-sink” problem for the nonlinear heat equation
نویسندگان
چکیده
منابع مشابه
the algorithm for solving the inverse numerical range problem
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 اولAn Inverse Problem for the Heat Equation
Let ut = uxx − q(x)u, 0 ≤ x ≤ 1, t > 0, u(0, t) = 0, u(1, t) = a(t), u(x, 0) = 0, where a(t) is a given function vanishing for t > T , a(t) 6≡ 0, ∫ T 0 a(t)dt < ∞. Suppose one measures the flux ux(0, t) := b0(t) for all t > 0. Does this information determine q(x) uniquely? Do the measurements of the flux ux(1, t) := b(t) give more information about q(x) than b0(t) does? The above questions are ...
متن کاملThe use of inverse quadratic radial basis functions for the solution of an inverse heat problem
In this paper, a numerical procedure for an inverse problem of simultaneously determining an unknown coefficient in a semilinear parabolic equation subject to the specification of the solution at an internal point along with the usual initial boundary conditions is considered. The method consists of expanding the required approximate solution as the elements of the inverse quadrati...
متن کاملAn inverse source problem for the heat equation and the enclosure method
An inverse source problem for the heat equation is considered. Extraction formulae for information about the time and location when and where the unknown source of the equation firstly appeared are given from a single lateral boundary measurement. New roles of the plane progressive wave solutions or their complex versions for the backward heat equation are given. AMS: 35R30, 80A23
متن کاملAn Inverse Problem for the Heat Equation Ii * †
Completeness of the set of products of the derivatives of the solutions to the equation (av′)′−λv = 0, v(0, λ) = 0 is proved. This property is used to prove the uniqueness of the solution to an inverse problem of finding conductivity in the heat equation u̇ = (a(x)u′)′, u(x, 0) = 0, u(0, t) = 0, u(1, t) = f(t) known for all t > 0, from the heat flux a(1)u′(1, t) = g(t). Uniqueness of the solutio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical and Computer Modelling
سال: 1993
ISSN: 0895-7177
DOI: 10.1016/0895-7177(93)90064-6