Global and blow-up radial solutions for quasilinear elliptic systems arising in the study of viscous, heat conducting fluids

AbstractIn this paper, we investigate the following quasilinear elliptic system (P) with explosive boundary conditions:ΔΔwhere Ω is a smooth bounded domain of ℝ

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High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: Viscous heat-conducting fluids and elastic solids

Journal of Computational Physics ◽

10.1016/j.jcp.2016.02.015 ◽

2016 ◽

Vol 314 ◽

pp. 824-862 ◽

Cited By ~ 75

Author(s):

Michael Dumbser ◽

Ilya Peshkov ◽

Evgeniy Romenski ◽

Olindo Zanotti

Keyword(s):

Continuum Mechanics ◽

High Order ◽

Heat Conducting ◽

Elastic Solids ◽

First Order ◽

Viscous Heat ◽

Heat Conducting Fluids ◽

Conducting Fluids

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Boundedness and blow-up of solutions for a nonlinear elliptic system

International Journal of Mathematics ◽

10.1142/s0129167x14500918 ◽

2014 ◽

Vol 25 (09) ◽

pp. 1450091 ◽

Cited By ~ 3

Author(s):

Dragos-Patru Covei

Keyword(s):

Stochastic Processes ◽

Elliptic System ◽

Blow Up ◽

Elliptic Systems ◽

Existence Results ◽

Nonlinear Elliptic System ◽

Unbounded Solutions ◽

Nonlinear Elliptic ◽

Quasilinear Elliptic Systems ◽

Quasilinear Elliptic

The main objective in this paper is to obtain the existence results for bounded and unbounded solutions of some quasilinear elliptic systems. Related results as obtained here have been established recently in [C. O. Alves and A. R. F. de Holanda, Existence of blow-up solutions for a class of elliptic systems, Differ. Integral Eqs.26(1/2) (2013) 105–118]. Also, we present some references to give the connection between these types of problems with probability and stochastic processes, hoping that these are interesting for the audience of analysts likely to read this paper.

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Existence of boundary blow-up solutions for a class of quasilinear elliptic systems with critical case

Applied Mathematics and Computation ◽

10.1016/j.amc.2007.08.074 ◽

2008 ◽

Vol 198 (2) ◽

pp. 574-581 ◽

Cited By ~ 5

Author(s):

Mingzhu Wu ◽

Zuodong Yang

Keyword(s):

Critical Case ◽

Blow Up ◽

Elliptic Systems ◽

Quasilinear Elliptic Systems ◽

Quasilinear Elliptic

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BLOW-UP OF SMOOTH SOLUTIONS TO THE NAVIER–STOKES EQUATIONS OF COMPRESSIBLE VISCOUS HEAT-CONDUCTING FLUIDS

Journal of the Australian Mathematical Society ◽

10.1017/s144678871000008x ◽

2010 ◽

Vol 88 (2) ◽

pp. 239-246 ◽

Cited By ~ 5

Author(s):

ZHONG TAN ◽

YANJIN WANG

Keyword(s):

Blow Up ◽

Stokes Equations ◽

Initial Density ◽

Navier Stokes ◽

Heat Conducting ◽

Smooth Solutions ◽

Navier Stokes Equations ◽

The Cauchy Problem ◽

Heat Conducting Fluids ◽

Conducting Fluids

AbstractWe give a simpler and refined proof of some blow-up results of smooth solutions to the Cauchy problem for the Navier–Stokes equations of compressible, viscous and heat-conducting fluids in arbitrary space dimensions. Our main results reveal that smooth solutions with compactly supported initial density will blow up in finite time, and that if the initial density decays at infinity in space, then there is no global solution for which the velocity decays as the reciprocal of the elapsed time.

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