On a criterion for the solvability of one ill-posed problem for the biharmonic equation

DOI10.1515/jiip-2016-0003zbMath1351.35021OpenAlexW2554007591MaRDI QIDQ2520120

Ulzada A. Iskakova, Makhmud A. Sadybekov, Tynysbek Sh. Kal'menov

Publication date: 13 December 2016

Published in: Journal of Inverse and Ill-Posed Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jiip-2016-0003

zbMATH Keywords

biharmonic equationasymptotics of eigenvaluesill-posed problemmethod of spectral decompositionspace of well-posedness

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Ill-posed problems for PDEs (35R25) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Strong solutions to PDEs (35D35)

Related Items (21)

Boundary conditions for the Cauchy potential for two-dimensional hyperbolic equations ⋮ On the symmetry of the boundary conditions of the volume potential ⋮ Solution of singularly perturbed Cauchy problem for ordinary differential equation of second order with constant coefficients by Fourier method ⋮ Regular boundary value problems for the heat equation with scalar parameters ⋮ On a class of inverse problems for a parabolic equation with involution ⋮ About characteristic determinant of one boundary value problem not having the basis property ⋮ On Hardy and Rellich type inequalities for an Engel-type operator ⋮ Volterra property of an problem of the Frankl type for an parabolic–hyperbolic equation ⋮ Trace formulae for the heat-volume potential of the time-fractional heat equation ⋮ Correct restrictions of first-order functional–differential equation ⋮ Basicity properties of eigenfunctions of the periodic problem for differential operator Lu = −u″(−x) + q(x)u(x) ⋮ On correct restrictions of bi-Laplace operator and their properties ⋮ On application of inverse problems with the nonlocal boundary conditions in the diffusion theory ⋮ On one inhomogeneous model of oscillations of a thin flat plate with a variety of mounts on opposite sides ⋮ Unnamed Item ⋮ A filter method with a priori and a posteriori parameter choice for the regularization of Cauchy problems for biharmonic equations ⋮ A method for solving ill-posed nonlocal problem for the elliptic equation with data on the whole boundary ⋮ Numerical solution of the nonlocal boundary value problem for elliptic equations ⋮ Direct and inverse problems for the Poisson equation with equality of flows on a part of the boundary ⋮ Representation of solution of the Dirichlet problem for the Laplace equation in the form of a generalized convolution ⋮ Regularized solution of an ill-posed biharmonic equation

Cites Work

• Unnamed Item
• Unnamed Item
• A method for solving the Cauchy problem for the Laplace equation
• A criterion for the strong solvability of the mixed Cauchy problem for the Laplace equation
• Comparative analysis of methods for regularizing an initial boundary value problem for the Helmholtz equation
• Regularization of the continuation problem for elliptic equations
• Inverse acoustic problems: theory and numerical methods
• On an ill-posed problem for a biharmonic equation

This page was built for publication: On a criterion for the solvability of one ill-posed problem for the biharmonic equation