Regularization and convergence for ill-posed backward evolution equations in Banach spaces. (English) Zbl 06901111
Summary: This work is concerned with a mathematical study of ill-posed backward evolution equations associated with densely defined linear differential operators in Banach spaces. A general approach is presented to investigate the convergence and stability of a class of regularized solutions for ill-posed backward evolution equations associated with sectorial or half-strip operators. Generalized concepts of qualification pairs and index functions are introduced to characterize the explicit convergence rates of the concerned regularized solutions. Applications of our results to general backward evolution equations are also investigated.
MSC:
| 65J20 | Numerical solutions of ill-posed problems in abstract spaces; regularization |
| 47A52 | Linear operators and ill-posed problems, regularization |
| 49J40 | Variational inequalities |
Keywords:
ill-posed backward evolution equations; sectorial operators; half-strip operators; regularizing family; convergence rates of regularized solutionsReferences:
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