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compressible Navier-Stokes equations with density-dependent
viscosity
Strongly nonlinear
multivalued systems involving singular $\Phi$-Laplacian operators
In this paper we study two vector problems with homogeneous
Dirichlet boundary conditions for second order strongly nonlinear
differential inclusions involving a maximal monotone term. The first
is governed by a nonlinear differential operator of the form
$x\mapsto (k(t)\Phi(x'))'$, where $k\in C(T, R_+)$ and $\Phi$ is an
increasing homeomorphism defined on a bounded domain. In this
problem the maximal monotone term need not be defined everywhere in
the state space $R^N$, incorporating into our framework
differential variational inequalities. The second problem is
governed by the more general differential operator of the type
$x\mapsto (a(t,x)\Phi(x'))'$, where $a(t,x)$ is a positive and
continuous scalar function. In this case the maximal monotone term
is required to be defined everywhere.