On certain mathematical models in continuum thermomechanics

[1]  D. Motreanu,et al.  A Generalized Phase-Field System☆ , 1999 .

[2]  Gonzalo Galiano,et al.  Existence and uniqueness of solutions of the Boussinesq system with nonlinear thermal diffusion , 1998 .

[3]  Songmu Zheng,et al.  Global Existence and Asymptotic Behavior in Nonlinear Thermoviscoelasticity , 1997 .

[4]  Eduard Feireisl,et al.  On the Navier-Stokes equations with temperature-dependent transport coefficients , 2006 .

[5]  Pavel E. Sobolevskii,et al.  Motion of nonlinear visco-elastic fluid , 1998 .

[6]  G. Caginalp An analysis of a phase field model of a free boundary , 1986 .

[7]  J. Rakotoson,et al.  A parabolic system involving a quadratic gradient term related to the Boussinesq approximation , 2007 .

[8]  Daniel D. Joseph,et al.  Stability of fluid motions , 1976 .

[9]  H. Triebel Interpolation Theory, Function Spaces, Differential Operators , 1978 .

[10]  Alessio Porretta,et al.  Existence results for nonlinear parabolic equations via strong convergence of truncations , 1999 .

[11]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[12]  Existence locale et unicit d'coulements de fluides viscolastiques dans des domaines non borns , 1999 .

[13]  D. Vorotnikov,et al.  On the solvability of the initial-value problem for the motion equations of nonlinear viscoelastic medium in the whole space , 2004 .

[14]  I. Pawlow,et al.  Unique solvability of a nonlinear thermoviscoelasticity system in Sobolev space with a mixed norm , 2010 .

[15]  J. Málek,et al.  On evolutionary Navier-Stokes-Fourier type systems in three spatial dimensions , 2011 .

[16]  Global existence for a hydrogen storage model with full energy balance , 2011, 1108.1332.

[17]  T. Roubicek,et al.  Thermo-visco-elasticity at small strains with ¹-data , 2009 .

[18]  Y. Shibata Global in time existence of small solutions of non‐linear thermoviscoelastic equations , 1995 .

[19]  K. Hoffmann,et al.  Existence of solutions to some non-linear thermoelastic systems with viscosity , 1992 .

[20]  Herbert Amann,et al.  Linear and Quasilinear Parabolic Problems: Volume I: Abstract Linear Theory , 1995 .

[21]  Donald M. Anderson,et al.  A phase-field model of solidification with convection , 2000 .

[22]  Tomáš Roubíček,et al.  Buoyancy-driven viscous flow with L L -data , 2001 .

[23]  Jürgen Sprekels,et al.  Global solutions to a model of structural phase transitions in shape memory alloys , 1988 .

[24]  Irena Pawlow,et al.  Global Regular Solutions to a Kelvin-Voigt Type Thermoviscoelastic System , 2013, SIAM J. Math. Anal..

[25]  A. Karma,et al.  Regular Article: Modeling Melt Convection in Phase-Field Simulations of Solidification , 1999 .

[26]  P. Lions,et al.  Ordinary differential equations, transport theory and Sobolev spaces , 1989 .

[27]  Clifford Ambrose Truesdell,et al.  A first course in rational continuum mechanics , 1976 .

[28]  Phase Transformations in Electrically Conductive Ferromagnetic Shape-Memory Alloys, Their Thermodynamics and Analysis , 2013 .

[29]  Christof Eck,et al.  Unilateral Contact Problems: Variational Methods and Existence Theorems , 2005 .

[30]  J. Cahn,et al.  A microscopic theory for antiphase boundary motion and its application to antiphase domain coasening , 1979 .

[31]  Luisa Consiglieri Weak Solutions for a Class of Non-Newtonian Fluids with Energy Transfer , 2000 .

[32]  L. Orsina,et al.  Nonlinear parabolic equations with natural growth conditions and L 1 data , 1996 .

[33]  K. R. Rajagopal,et al.  Mathematical Analysis of Unsteady Flows of Fluids with Pressure, Shear-Rate, and Temperature Dependent Material Moduli that Slip at Solid Boundaries , 2009, SIAM J. Math. Anal..

[34]  D. Blanchard,et al.  Weak-renormalized solution for a nonlinear Boussinesq system , 2009, Differential and Integral Equations.

[35]  T. Gallouët,et al.  Non-linear elliptic and parabolic equations involving measure data , 1989 .

[36]  John M. Mihaljan,et al.  A Rigorous Exposition of the Boussinesq Approximations Applicable to a Thin Layer of Fluid. , 1962 .

[37]  D. Blanchard,et al.  Renormalized solutions for a class of nonlinear evolution problems , 1998 .

[38]  D. Vorotnikov,et al.  Approximating-topological methods in some problems of hydrodynamics , 2008 .

[39]  M. Frémond,et al.  Non-Smooth Thermomechanics , 2001 .

[40]  J. E. Hilliard,et al.  Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .

[41]  Luisa Consiglieri Friction boundary conditions on thermal incompressible viscous flows , 2008 .

[42]  P. Lions Mathematical topics in fluid mechanics , 1996 .

[43]  Stephan Luckhaus,et al.  Quasilinear elliptic-parabolic differential equations , 1983 .

[44]  E. Fernández-Cara,et al.  Weak-renormalized solutions for a system that models non-isothermal solidification , 2012 .

[45]  D. Blanchard,et al.  Existence and Uniqueness of a Renormalized Solution for a Fairly General Class of Nonlinear Parabolic Problems , 2001 .

[46]  G. Caginalp,et al.  A Derivation and Analysis of Phase Field Models of Thermal Alloys , 1995 .

[47]  On non-Newtonian Fluids with Energy Transfer , 2009 .

[48]  Herbert Amann,et al.  Abstract linear theory , 1995 .

[49]  Luisa Consiglieri REGULARITY FOR THE NAVIER-STOKES-FOURIER SYSTEM , 2009 .

[50]  Y. Kagei,et al.  Natural Convection with Dissipative Heating , 2000 .

[51]  P. Lions,et al.  On the Cauchy problem for Boltzmann equations: global existence and weak stability , 1989 .

[52]  E. Fernández-Cara,et al.  Some existence and uniqueness results for a time-dependent coupled problem of the Navier-Stokes kind , 1998 .

[53]  Existence and uniqueness of the solution of a Boussinesq system with nonlinear dissipation , 2013 .

[54]  Tomáš Roubíček,et al.  Nonlinearly coupled thermo-visco-elasticity , 2013 .

[55]  E. Fernández-Cara,et al.  Existence and uniqueness results for a coupled problem related to the stationary Navier-Stokes system , 1997 .

[56]  M. Ružička,et al.  Mathematical modeling of electrorheological materials , 2001 .

[57]  EXISTENCE AND UNIQUENESS OF THE SOLUTION TO A 3D THERMOVISCOELASTIC SYSTEM , 2003 .

[58]  T. Gallouët,et al.  Nonlinear Parabolic Equations with Measure Data , 1997 .

[59]  Herbert Amann,et al.  Linear and Quasilinear Parabolic Problems , 2019, Monographs in Mathematics.

[60]  J. Prüss,et al.  Optimal Lp-Lq-estimates for parabolic boundary value problems with inhomogeneous data , 2007 .

[61]  D. Blanchard,et al.  Renormalised solutions of nonlinear parabolic problems with L1 data: existence and uniqueness , 1997, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[62]  P. Sobolevskiĭ,et al.  COERCIVENESS INEQUALITIES FOR ABSTRACT PARABOLIC EQUATIONS , 1964 .

[63]  D. Blanchard,et al.  Existence of a solution for a nonlinear system in thermoviscoelasticity , 2000, Advances in Differential Equations.

[64]  J. Naumann On the existence of weak solutions to the equations of non-stationary motion of heat-conducting incompressible viscous fluids , 2006 .