The aim of this article is to discuss strong solutions of doubly nonlinear parabolic equations
where and are operators satisfying standard assumptions on boundedness, coercivity and monotonicity. Six different situations are identified which allow to prove the existence of a solution to an initial value , but only in some of these situations the equation is valid in a stronger space than .
Cite this article
Aleš Matas, Jochen Merker, Strong Solutions of Doubly Nonlinear Parabolic Equations. Z. Anal. Anwend. 31 (2012), no. 2, pp. 217–235DOI 10.4171/ZAA/1456