Integral identity for a class of ill-posed problems generated by a parabolic equation
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Sergey A. Vavilov
Abstract
The goal of the present study is to derive an integral identity for a class of ill-posed problems generated by a parabolic equation. The obtained result enables us to reduce the original ill-posed problem directly to the first-kind Fredholm equation with translation kernel. Various real world applications to a different fields of knowledge, including ecology and finances, are presented.
Acknowledgements
The authors are grateful to professor V. G. Osmolovskii for his interest to the paper and valuable comments.
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© 2016 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- A finite element method for the inverse problem of boundary data recovery in an oxygen balance model
- On regularization and error estimates for the Cauchy problem of the modified inhomogeneous Helmholtz equation
- Application of the factorization method to retrieve a crack from near field data
- Solution to a class of inverse problems for a system of loaded ordinary differential equations with integral conditions
- The variational formulation of an inverse problem for multidimensional nonlinear time-dependent Schrödinger equation
- Integral identity for a class of ill-posed problems generated by a parabolic equation
- A meshless method to the solution of an ill-posed problem
- About an inverse problem for a free boundary compressible problem in hydrodynamic lubrication
- Error analysis for the operator marching method applied to range dependent waveguides
Artikel in diesem Heft
- Frontmatter
- A finite element method for the inverse problem of boundary data recovery in an oxygen balance model
- On regularization and error estimates for the Cauchy problem of the modified inhomogeneous Helmholtz equation
- Application of the factorization method to retrieve a crack from near field data
- Solution to a class of inverse problems for a system of loaded ordinary differential equations with integral conditions
- The variational formulation of an inverse problem for multidimensional nonlinear time-dependent Schrödinger equation
- Integral identity for a class of ill-posed problems generated by a parabolic equation
- A meshless method to the solution of an ill-posed problem
- About an inverse problem for a free boundary compressible problem in hydrodynamic lubrication
- Error analysis for the operator marching method applied to range dependent waveguides
