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On the Cauchy problem for semilinear elliptic equations
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Nguyen Huy Tuan
Published/Copyright:
November 25, 2015
Abstract
We study the Cauchy problem for nonlinear (semilinear) elliptic partial differential equations in Hilbert spaces. The problem is severely ill-posed in the sense of Hadamard. Under a weak a priori assumption on the exact solution, we propose a new regularization method for stabilising the ill-posed problem. These new results extend some earlier works on Cauchy problems for nonlinear elliptic equations. Numerical results are presented and discussed.
Funding source: Foundation for Science and Technology Development of Ton Duc Thang University
Award Identifier / Grant number: FOSTECT.2014.BR.03
Funding source: Seoul National University
Award Identifier / Grant number: Research Grant
Received: 2015-6-4
Accepted: 2015-9-19
Published Online: 2015-11-25
Published in Print: 2016-4-1
© 2016 by De Gruyter
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Keywords for this article
Cauchy problem;
nonlinear elliptic equation;
ill-posed problem;
error estimates
Articles in the same Issue
- Frontmatter
- Preface
- In celebration of the 60th birthday of Professor Alemdar Hasanoğlu (Hasanov)
- An inverse source problem for a damped wave equation with memory
- On the Cauchy problem for semilinear elliptic equations
- A unified approach to convergence rates for ℓ1-regularization and lacking sparsity
- Regularization of ill-posed problems by using stabilizers in the form of the total variation of a function and its derivatives
- Numerical testing in determination of sound speed from a part of boundary by the BC-method
- Inverse determination of spatially varying material coefficients in solid objects
- Determination of the initial condition in parabolic equations from boundary observations
