منابع مشابه
An Inverse Problem for an Abstract Evolution Equation
The inverse problem of finding the coefficient γ in the equation u̇ = A(t)u + γ(t)u + f(t) from the extra data of the form φ(t) = 〈u(t), w〉 is studied. The problem is reduced to a Volterra equation of the second kind. Applications are given to parabolic equations with second order differential operators.
متن کاملAn Inverse Problem for the Telegraph Equation
This paper deals with the problem of state estimation for a hyperbolic equation in the presence of unknown, but bounded disturbances, on the basis of information from sensors with finite-dimensional outputs. The object of investigation is the hyperbolic telegraph equation with energy dissipation. Observability properties similar to those introduced earlier for parabolic systems ([8]) are checke...
متن کاملAn 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 کاملInverse Problem for an Inhomogeneous Schrödinger Equation * †
Let (− k 2)u = −u + q(x)u − k 2 u = δ(x), x ∈ R, ∂u ∂|x| − iku → 0, |x| → ∞. Assume that the potential q(x) is real-valued and compactly supported: q(x) = q(x), q(x) = 0 for |x| ≥ 1, 1 −1 |q|dx < ∞, and that q(x) produces no bound states. Let u(−1, k) and u(1, k) ∀k > 0 be the data. Theorem.Under the above assumptions these data determine q(x) uniquely.
متن کاملAn inverse problem for Helmholtz equation
This article is concerned with subsurface material identification for the 2-D Helmholtz equation. The algorithm is iterative in nature. It assumes an initial guess for the unknown function and obtains corrections to the guessed value. It linearizes the otherwise nonlinear problem around the background field. The background field is the field variable generated using the guessed value of the unk...
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: Applicable Analysis
سال: 2001
ISSN: 0003-6811,1563-504X
DOI: 10.1080/00036810108840973