Strong Solutions of Doubly Nonlinear Parabolic Equations

  • Aleš Matas

    University of West-Bohemia, Pilsen, Czech Republic
  • Jochen Merker

    Universität Rostock, Germany


The aim of this article is to discuss strong solutions of doubly nonlinear parabolic equations

But+Au=f,\frac{\partial Bu}{\partial t} + Au = f,

where A:XXA : X → X^* and B:YYB : Y → Y^* are operators satisfying standard assumptions on boundedness, coercivity and monotonicity. Six different situations are identified which allow to prove the existence of a solution uL(0,T;XY)u ∈ L^∞(0,T;X ∩ Y) to an initial value u0XYu_0 ∈ X ∩ Y, but only in some of these situations the equation is valid in a stronger space than (XY)(X ∩ Y)^*.

Cite this article

Aleš Matas, Jochen Merker, Strong Solutions of Doubly Nonlinear Parabolic Equations. Z. Anal. Anwend. 31 (2012), no. 2, pp. 217–235

DOI 10.4171/ZAA/1456