Vanishing latent heat limit in a Stefan-like problem arising in biology (original) (raw)
Asymptotic behavior of solutions to a multi-phase Stefan problem
Japan Journal of Applied Mathematics, 1986
This paper is concerned with the asymptotic behavior of weak solutions to a multi-phase Stefan problem for a quasi-linear heat equation of the form p(v) t -Av =fin several space variables, with Dirichlet-Neumann boundary condition on the fixed boundary. We shall discuss the asymptotic convergence of the enthalpy and temperature in L2(O) and H~(12), respectiwly, when the prescribed boundary data asymptoticaUy converge in some sense. Our approach to the investigation of the asymptotic convergence of solutions is based on the theory of nonlinear evolution equations governed by time-dependent subdifferential operators in Hilbert spaces. The results obtained in this paper improve on those established so far.
Spatial segregation limit of a competition–diffusion system
European Journal of Applied Mathematics, 1999
We consider a competition–diffusion system and study its singular limit as the interspecific competition rate tend to infinity. We prove the convergence to a Stefan problem with zero latent heat.
Journal of Mathematical Analysis and Applications, 2012
Stefan problem Free boundary problems Heat transfer coefficient Asymptotic behavior Order of convergence We consider the one-phase unidimensional Stefan problem with a convective boundary condition at the fixed face, with a heat transfer coefficient (proportional to the Biot number) h > 0. We study the limit of the temperature θ h and the free boundary s h when h goes to zero, and we also obtain an order of convergence. The goal of this paper is to do the mathematical analysis of the physical behavior given in [C. Naaktgeboren, The zero-phase Stefan problem, Int. J. Heat Mass Transfer 50 4614-4622].
Stefan — like problems with space — dependent latent heat
Meccanica, 1970
SOMMARIO: Si stndia una vasta classe di problemi di conduzione unidimensiona/e det catore in presenza di cambiamento di fase, nel caso in cui il calore /atente sia funzione della posizione del fronte di separazione Ira /e dne fasi: L = cF[s(t)]. Si trovano delle condizioni sufflcienti per l'esistenza e la unicith delta soluzione del prob/ema in un certo intervallo di tempo; si moslra infine chela trattazione permette di generalizzare risu#ati giit noti e di estendere lo studio a casi di particolare inleresse. SUMMARY: A wide class of one-dimensional heat conduction problems with phase change is considered on the assumption that the latent heat is a given function of the position of the separation plane bet,veen the hvo phases: L = ~[s(t)]. Some snfficient conditions for the existence and uniqueness of the solution in a given time-interval are given. This work permits the genera/izalion of some previons results attd the investigation of some cases of particular interest.
Free Boundary Convergence in the Homogenization of the One Phase Stefan Problem
Transactions of The American Mathematical Society, 1982
We consider the one phase Stefan problem in a "granular" medium, i.e., with nonconstant thermal diffusity, and we study the asymptotic behaviour of the free boundary with respect to homogenization. We prove the convergence of the coincidence set in measure and in the Hausdorff metric. We apply this result to the free boundary and we obtain the convergence in mean for the star-shaped case and the uniform convergence for the one-dimensional case, respectively. This gives an answer to a problem posed by J. L. Lions in [L].
Singular limits for the two-phase Stefan problem
Discrete and Continuous Dynamical Systems, 2013
We prove strong convergence to singular limits for a linearized fully inhomogeneous Stefan problem subject to surface tension and kinetic undercooling effects. Different combinations of σ → σ 0 and δ → δ 0 , where σ, σ 0 ≥ 0 and δ, δ 0 ≥ 0 denote surface tension and kinetic undercooling coefficients respectively, altogether lead to five different types of singular limits. Their strong convergence is based on uniform maximal regularity estimates.
Regularity of weak solutions of one-dimensional two-phase Stefan problems
Annali di Matematica Pura ed Applicata, Series 4, 1977
Sunto.-Si consldera il problems di Ste]an unidimensiona~v a duv ]asl e si dimostra ~'esistenza di soluzio~d vlasslche sotto ipotesi minimali sui dat~ (continuit~ a tratti e limitatezza). 2~elle stesse ipotesl sl dlmostra vhe tall soluzloni dipendono iv~ modo conti'~uo da~ dati, conseguendo un visultato che $ pi~ generale anvhe di quelto noto pet le sohtzioni deboli. l.-Introduction.
Continuity for bounded solutions of multiphase Stefan problem
1994
Equazioni a derivate parziali.-Continuity for bounded solutions of multiphase Stefan problem. Nota di EMMANUELE DIBENEDETTO e VINCENZO VESPRI, presentata!") dal Socio E. Magenes. ABSTRACT.-We establish the continuity of bounded local solutions of the equation ji(u) t = ku. Here /3 is any coercive maximal monotone graph inlxR, bounded for bounded values of its argument. The multiphase Stefan problem and the Buckley-Leverett model of two immiscible fluids in a porous medium give rise to such singular equations. KEY WORDS: Singular parabolic equations; Regularity; Stefan problem; Maximal monotone graphs. RIASSUNTO.-Continuità per soluzioni limitate del problema di Stefan multifase. In questa Nota si dimostra la continuità delle soluzioni locali limitate dell'equazione @(u) t = Au, dove p è un qualsiasi grafo massimale monotono e coercivo in R X R, che si mantiene limitato per valori limitati del suo argomento. A questo contesto appartengono sia il problema di Stefan multifase che il modello di Buckley-Leverett di due fluidi immiscibili in un mezzo poroso.