# Strong Solutions of Doubly Nonlinear Parabolic Equations

### Aleš Matas

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

Universität Rostock, Germany

## Abstract

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

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

where $A : X → X^*$ and $B : Y → Y^*$ are operators satisfying standard assumptions on boundedness, coercivity and monotonicity. Six different situations are identified which allow to prove the existence of a solution $u ∈ L^∞(0,T;X ∩ Y)$ to an initial value $u_0 ∈ X ∩ Y$, but only in some of these situations the equation is valid in a stronger space than $(X ∩ Y)^*$.

## 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