Continuous dependence on modeling for nonlinear ill-posed problems

DOI10.1016/J.JMAA.2008.08.052zbMath1169.34042OpenAlexW2170651764MaRDI QIDQ953506

Rhonda J. Hughes, Beth M. Campbell Hetrick

Publication date: 6 November 2008

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2008.08.052

zbMATH Keywords

abstract Cauchy problemnonlinear ill-posed problemcontinuous depending on modeling

Mathematics Subject Classification ID

Nonlinear differential equations in abstract spaces (34G20)

Related Items (11)

Logarithmic well-posed approximation of the backward heat equation in Banach space ⋮ Backward heat equations with locally lipschitz source ⋮ Ill-posed problems associated with sectorial operators in Banach space ⋮ Convergence rates for solutions of inhomogeneous ill-posed problems in Banach space with sufficiently smooth data ⋮ Regularization of an inverse nonlinear parabolic problem with time-dependent coefficient and locally Lipschitz source term ⋮ A new Fourier truncated regularization method for semilinear backward parabolic problems ⋮ On a backward Cauchy problem associated with continuous spectrum operator ⋮ Stability in Kelvin-Voigt poroelasticity ⋮ On a backward parabolic problem with local Lipschitz source ⋮ The backward problem for Ginzburg-Landau-type equation ⋮ Estimates for solutions of nonautonomous semilinear ill-posed problems

Cites Work

• Continuous dependence results for inhomogeneous ill-posed problems in Banach space
• Semigroups of linear operators and applications to partial differential equations
• The final value problem for evolution equations
• Logarithmic convexity results for holomorphic semigroups
• Structural stability for ill-posed problems in Banach space
• On the Comparison of Solutions of Related Properly and Improperly Posed Cauchy Problems for First Order Operator Equations
• A comparison of regularizations for an ill-posed problem
• Lower Bounds and Uniqueness Theorems for Solutions of Differential Equations in a Hilbert Space
• Properties of solutions of ordinary differential equations in banach space
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