Many methods of material characterization by rheological methods lead
to ill-posed problems. The nature of ill-posedness is discussed. In th
is light, some such new problems appearing in molecular weight charact
erization of homopolymers as well as in the characterization of size d
istribution of dispersed phases in polymer blends by rheological techn
iques are analyzed. The working capability of a nonlinear regularizati
on method is demonstrated with examples of blend theology. The role of
Professor Meissner in motivating the research in the field of ill-pos
ed problems as well as his important contribution to rheology of polym
er blends is outlined.