Steady-state buoyancy-driven viscous flow with measure data

Tomáš Roubíček

Displaying similar documents to “Steady-state buoyancy-driven viscous flow with measure data”

Optimal Convective Heat-Transport

Josef Dalík, Oto Přibyl (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The one-dimensional steady-state convection-diffusion problem for the unknown temperature $y (x)$ of a medium entering the interval $(a, b)$ with the temperature $y_{min}$ and flowing with a positive velocity $v (x)$ is studied. The medium is being heated with an intensity corresponding to $y_{max} - y (x)$ for a constant $y_{max} > y_{min}$ . We are looking for a velocity $v (x)$ with a given average such that the outflow temperature $y (b)$ is maximal and discuss the influence of the boundary condition at the point $b$ on the “maximizing” function $v (x)$ . ...

On the existence of a generalized solution to a three-dimensional elliptic equation with radiation boundary condition

László Simon, Gisbert Stoyan (2001)

Applications of Mathematics

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For a second order elliptic equation with a nonlinear radiation-type boundary condition on the surface of a three-dimensional domain, we prove existence of generalized solutions without explicit conditions (like ${u |}_{Γ} \in L_{5} (Γ)$ ) on the trace of solutions. In the boundary condition, we admit polynomial growth of any fixed degree in the unknown solution, and the heat exchange and emissivity coefficients may vary along the radiating surface. Our generalized solution is contained in a Sobolev space with...

Non-existence of global classical solutions to 1D compressible heat-conducting micropolar fluid

Jianwei Dong, Junhui Zhu, Litao Zhang (2024)

Czechoslovak Mathematical Journal

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We study the non-existence of global classical solutions to 1D compressible heat-conducting micropolar fluid without viscosity. We first show that the life span of the classical solutions with decay at far fields must be finite for the 1D Cauchy problem if the initial momentum weight is positive. Then, we present several sufficient conditions for the non-existence of global classical solutions to the 1D initial-boundary value problem on $[0, 1]$ . To prove these results, some new average quantities...