On stationary thermo-rheological viscous flows

By Stanislav N. Antontsev, J. Rodrigues. 2006

429 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/cc03eabac04344f3af96710950114c2b0ba9e4c0

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Solvability of the three-dimensional thermistor problem (2008, background): “Such systems and especially hydromechanical systems with similar structure have attracted much attention in recent years (see [1–6] and the references therein).”
Three solutions for a nonlocal Dirichlet boundary value problem involving the p(x)-Laplacian (2013, background): “Problems with variable exponent growth conditions also appear in the mathematical modelling of stationary thermo-rheological viscous flows of non-Newtonian fluids and in the mathematical description of the processes filtration of ideal barotropic gas through a porous medium 3 , 4 .”
Anisotropic parabolic equations with variable nonlinearity (2009, background): “Equations of the type (1.1) and their elliptic counterparts appear in the mathematical descriptions of motions of the non‐newtonian fluids [ 17 ], in particular, electro‐rheological fluids which are characterized by their ability to change the mechanical properties under the influence of the exterio”
Overview of differential equations with non-standard growth (2010, background): “Finally, Růžička and his collaborators [22, 23] studied equations with non-standard growth in the modeling of so-called electrorheological fluids, see also [29, 31, 40].”
Wulff shape characterizations in overdetermined anisotropic elliptic problems (2017, background): “For instance, in deformation theory of plasticity E and J represent the infinitesimal strain and stress [44, 50], respectively, for nonlinear dielectrics problems E and J are the electric field and current [19, 25, 34], respectively, and this types of laws arise also in fluid flows where E and J are”
Wave Equation with p(x,t) - Laplacian and Damping Term: Existence and Blow-up (2011, background): “, [5, 6, 8, 35, 36] ) and the further references therein).”
Existence and multiplicity results for a newp(x)-Kirchhoff problem (2019, background): “In the studies of a class of non-standard variational problems and PDEs, variable exponent spaces play an important role for example, in electrorheological fluids [36, 35, 34], thermorheological fluids [6], image processing [1, 9, 28], etc.”
The obstacle problem for nonlinear elliptic equations with variable growth and L1-data (2008, background): “Recent applications in elasticity [32], non–Newtonian fluid mechanics [33, 30, 5 ], or image processing [13], gave rise to a revival of the interest in these spaces, the origins of which can be traced back to the work of Orlicz in the 1930’s.”