Two regularized solutions of an ill-posed problem for the elliptic equation with inhomogeneous source
نویسندگان
چکیده
منابع مشابه
Irregular Solutions of an Ill-Posed Problem
Tikhonov regularization is a popular and effective method for the approximate solution of illposed problems, including Fredholm equations of the first kind. The Tikhonov method works well when the solution of the equation is well-behaved, but fails for solutions with irregularities, such as jump discontinuities. In this paper we develop a method that overcomes the limitations of the standard Ti...
متن کاملMultiple solutions for an inhomogeneous semilinear elliptic equation in R
In this paper, we will investigate the existence of multiple solutions for the general inhomogeneous elliptic problem − u+ u = f (x, u) + μh (x) , x ∈ R , u ∈ H (RN) , (1.1)μ where h ∈ H−1 (RN), N ≥ 2, |f (x, u)| ≤ C1up−1 + C2u with C1 > 0, C2 ∈ [0, 1) being some constants and 2 < p < +∞. ∗Research supported in part by the Natural Science Foundation of China and NSEC †Research supported ...
متن کاملOptimal Control of an Ill Posed Elliptic Semilinear Equation with an Exponential Non Linearity
We study here an optimal control problem for a semilinear elliptic equation with an exponential nonlinearity such that we cannot expect to have a solution of the state equation for any given control We then have to speak of pairs control state After having de ned a suit able functional class in which we look for solutions we prove existence of an optimal pair for a large class of cost functions...
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 کاملAn Iteratively Regularized Projection Method for Nonlinear Ill-posed Problems
An iterative regularization method in the setting of a finite dimensional subspace Xh of the real Hilbert space X has been considered for obtaining stable approximate solution to nonlinear ill-posed operator equations F (x) = y where F : D(F ) ⊆ X −→ X is a nonlinear monotone operator on X. We assume that only a noisy data yδ with ‖y − yδ‖ ≤ δ are available. Under the assumption that the Fréche...
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: 2014
ISSN: 0354-5180,2406-0933
DOI: 10.2298/fil1410091t