Global solvability and asymptotic behavior of a free boundary problem for the one-dimensional viscous radiative and reactive gas

2012 ◽  
Vol 53 (12) ◽  
pp. 123704 ◽  
Author(s):  
Jie Jiang ◽  
Songmu Zheng
Keyword(s):  
Asymptotic Behavior ◽  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Global Solvability ◽  
One Dimensional ◽  
The One ◽  
A Free Boundary Problem ◽  
Reactive Gas

scholarly journals Global Solvability of Compressible–Incompressible Two-Phase Flows with Phase Transitions in Bounded Domains

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 258
Author(s):  
Keiichi Watanabe
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Global Solvability ◽  
Time Interval ◽  
Bounded Domains ◽  
Two Phase Flows ◽  
Two Phase ◽  
Unique Existence ◽  
A Free Boundary Problem

Consider a free boundary problem of compressible-incompressible two-phase flows with surface tension and phase transition in bounded domains Ωt+,Ωt−⊂RN, N≥2, where the domains are separated by a sharp compact interface Γt⊂RN−1. We prove a global in time unique existence theorem for such free boundary problem under the assumption that the initial data are sufficiently small and the initial domain of the incompressible fluid is close to a ball. In particular, we obtain the solution in the maximal Lp−Lq-regularity class with 2<p<∞ and N<q<∞ and exponential stability of the corresponding analytic semigroup on the infinite time interval.

A free boundary problem arising in the modelling of internal oxidation of binary alloys

1995 ◽  
Vol 6 (3) ◽  
pp. 225-245
Author(s):  
Bei Hu ◽  
Jianhua Zhang
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Internal Oxidation ◽  
Free Boundary Problem ◽  
Binary Alloys ◽  
Local Existence ◽  
Discontinuous Coefficients ◽  
Parabolic Partial Differential Equation ◽  
One Dimensional ◽  
A Free Boundary Problem

A one-dimensional free boundary problem arising in the modelling of internal oxidation of binary alloys is studied in this paper. The free boundary of this problem is determined by the equation u = 0, where u is the solution of a parabolic partial differential equation with discontinuous coefficients across the free boundary. Local existence, uniqueness and the regularity of the free boundary are established. Global existence is also studied.

Gelification and mass transport in a static non-isothermal waxy solution

2009 ◽  
Vol 20 (1) ◽  
pp. 93-122 ◽  
Author(s):  
A. FASANO ◽  
L. FUSI ◽  
J. R. OCKENDON ◽  
M. PRIMICERIO
Keyword(s):  
Free Boundary ◽  
Mass Transport ◽  
Boundary Problem ◽  
Cloud Point ◽  
Free Boundary Problem ◽  
Mathematical Problem ◽  
Well Posedness ◽  
Dimensional Model ◽  
One Dimensional ◽  
A Free Boundary Problem

We consider a solution of a mono-component oil and wax. The latter is dissolved in the oil if the temperature is above the so-called cloud point (which depends on the concentration) and it segregates in the form of solid crystals if temperature is below the cloud point. As the solid fraction of wax increases, the diffusivity of liquid wax in the oil decreases (gelification), eventually vanishing. We study a one-dimensional model where temperature is initially above the cloud point and then it is lowered to induce diffusion and gelification. We formulate the relevant mathematical problem (a free boundary problem), studying its well-posedness and showing some qualitative results.

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