Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6417952 | Journal of Mathematical Analysis and Applications | 2015 | 24 Pages |
We extract rates of convergence and rates of metastability (in the sense of Tao) for convergence results regarding abstract Cauchy problems generated by Ï-accretive at zero operators A:D(A)(âX)â2X where X is a real Banach space, proved in [8], by proof-theoretic analysis of the proofs in [8] and having assumed a new, stronger notion of uniform accretivity at zero, yielding a new notion of modulus of accretivity. We compute the rate of metastability for the convergence of the solution of the abstract Cauchy problem generated by a uniformly accretive at zero operator to the unique zero of A via proof mining based on a result by the first author. Finally, we apply our results to a special class of Cauchy problems considered in [8]. This work is the first application of proof mining to the theory of partial differential equations.