Continuous Dependence on Modeling for Related Cauchy Problems of a Class of Evolution Equations

Solutions of a class of Cauchy problems are compared with solutions of related perturbed problems. H¨older continuous dependence on the perturbation parameter is established for the difference of these solutions using the logarithmic convexity method. Results are also obtained under weaker restrictions for a special class of linear equations by employing the Lagrange identity method. Studies of this kind attempt to regularize problems that may be ill posed against errors made in formulating the governing equations of mathematical models.