Calculation of anomalous exponents in nonlinear diffusion
D. G. Aronson, J. L. Vazquez · Physical Review Letters · 1994
We present a rigorous method based on the implicit function theorem for computing anomalous exponents for self-similar solutions to a variety of problems in continuum mechanics. Unlike formal perturbation methods which give only local results, our method often gives global results and analytic dependence of the exponent on parameters. We describe in detail the application of the method to source-type solutions to Barenblatt's equation for elastoplastic flow, a problem which has been treated elsewhere by renormalization methods. We also briefly describe several other applications.