in this paper, a nonlinear inverse problem of parabolic type, is considered. by reducing this inverse problem to a system of volterra integral equations the existence, uniqueness, and stability of the solution will be shown.

where A is some set of multiindices α. A first crucial question is whether there is enough data to (uniquely) find f . Let u0 be a function in the Sobolev space H(Ω) with zero Cauchy data u0 = ∂νu0 = 0 on Γ0 and let f0 = −∆u0. Due to linearity, −∆(u+ u0) = f + f0. Obviously, u and u+ u0 have the same Cauchy data on Γ0, so f and f+f0 produce the same data (2), but they are different in Ω. It is ...

Nonnegative matrices have long been a sorce of interesting and challenging mathematical problems. They are real matrices with all their entries being nonnegative and arise in a num‐ ber of important application areas: communications systems, biological systems, economics, ecology, computer sciences, machine learning, and many other engineering systems. Inverse eigenvalue problems constitute an ...

1 Introduction The inverse spectral problem on a Riemannian manifold (M, g), possibly with boundary, is to determine as much as possible of the geometry of (M, g) from the spectrum of its Laplacian ∆ g (with some given boundary conditions). The special inverse problem of Kac is to determine a Euclidean domain Ω ⊂ R n up to isometry from the spectrum Spec B (Ω) of its Laplacian ∆ B with Dirichle...

in this work, a direct design approach for designing a surface shape (inverse design problem) has been developed, in which both the target surface pressure and the unknown nodal coordinates appear explicitly in the formulations. the final discretized form of the governing equations (unified formulation) can be used for both analysis and shape design problems. in this work, shape design problems...

‎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...

Stereology is the part of imaging science in which the three-dimensional structure of a body is determined from two-dimensional views. Although it is relatively easy to determine volume information from 2-D slices, it is nontrivial in general to determine other physical properties such as internal surface areas unless the medium is known to have some simple symmetry such as isotropy. For this r...

Let F be a family of subsets of the ground set [n] = {1, 2, . . . , n}. For each i ∈ [n] we let p(F , i) be the number of pairs of subsets that differ in the element i and exactly one of them is in F . We interpret p(F , i) as the influence of that element. The normalized Banzhaf vector of F , denoted B(F), is the vector (B(F , 1), . . . , B(F , n)), where B(F , i) = p(F ,i) p(F) and p(F) is th...