On an ill-posed problem for a biharmonic equation
نویسندگان
چکیده
منابع مشابه
An ill-posed boundary value problem for the Helmholtz equation on Lipschitz domains
The paper is concerned with properties of an ill-posed problem for the Helmholtz equation when Dirichlet and Neumann conditions are given only on a part Γ of the boundary ∂Ω. We present an equivalent formulation of this problem in terms of a moment problem defined on the part of the boundary where no boundary conditions are imposed. Using a weak definition of the normal derivative, we prove the...
متن کاملA comparison of regularizations for an ill-posed problem
We consider numerical methods for a “quasi-boundary value” regularization of the backward parabolic problem given by { ut + Au = 0 , 0 < t < T u(T ) = f, where A is positive self-adjoint and unbounded. The regularization, due to Clark and Oppenheimer, perturbs the final value u(T ) by adding αu(0), where α is a small parameter. We show how this leads very naturally to a reformulation of the pro...
متن کاملA Finite Element Method for an Ill-Posed Problem
For an ill-posed problem which has its origin in several applications (e.g. electro-cardiology) a weak formulation is given over a Hilbert space without any constraints. This is achieved by means of Lagrangian multipliers. Beside theoretical questions (e.g. existence and uniqueness of a solutuion) a nite element approximation is considered. Error estimates, an investigation of the condition num...
متن کاملAn ill-posed mechanical problem with friction
Many models involve the Coulomb’s law in order to describe dynamical properties of friction phenomena. In order to generalize this Coulomb’s law and to deal with its correct mathematical expression, we study a nonlinear equation where we take into account a maximal monotone graph. In the particular case of Coulomb’s law, existence and uniqueness are proved. But in the general case, only existen...
متن کاملA Numerical Method for an Ill-posed Problem
The noncharacterisitic initial value problem for the one-dimensional heat equation (the solution and its rst-order spatial derivative speciied on an interval of the time axis) is well known to be ill-posed. Nevertheless, the author has proved in 4] that nonnegative solutions of this problem depend continuously on the initial data. However, this result does not solve the problem of constructing ...
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: Filomat
سال: 2017
ISSN: 0354-5180,2406-0933
DOI: 10.2298/fil1704051k