Nonlinear systems of parabolic PDE's for phase change problem
Kenmochi, Nobuyuki
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Kenmochi, Nobuyuki
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Changchun Liu (2013)
Annales Polonici Mathematici
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We consider an initial-boundary problem for a sixth order nonlinear parabolic equation, which arises in oil-water-surfactant mixtures. Using Schauder type estimates and Campanato spaces, we prove the global existence of classical solutions for the problem in two space dimensions.
Andrzej Raczyński (2004)
Banach Center Publications
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We study the existence of solutions to a nonlinear parabolic equation describing the temporal evolution of a cloud of self-gravitating particles with a given external potential. The initial data are in spaces of (generalized) pseudomeasures. We prove existence of local and global-in-time solutions, and also a kind of stability of global solutions.
Carole Rosier, Lionel Rosier (2004)
Banach Center Publications
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Results on the global existence and uniqueness of variational solutions to an elliptic-parabolic problem occurring in statistical mechanics are provided.
Michele Colturato (2016)
Applications of Mathematics
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We consider a phase-field system of Caginalp type perturbed by the presence of an additional maximal monotone nonlinearity. Such a system arises from a recent study of a sliding mode control problem. We prove the existence of strong solutions. Moreover, under further assumptions, we show the continuous dependence on the initial data and the uniqueness of the solution.
Piotr Biler (1995)
Studia Mathematica
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The existence of solutions to the Cauchy problem for a nonlinear parabolic equation describing the gravitational interaction of particles is studied under minimal regularity assumptions on the initial conditions. Self-similar solutions are constructed for some homogeneous initial data.
Piotr Biler, Tadeusz Nadzieja (1995)
Applicationes Mathematicae
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Radially symmetric solutions of a nonlocal Fokker-Planck equation describing the evolution of self-attracting particles in a bounded container are studied. Conditions ensuring either global-in-time existence of solutions or their finite time blow up are given.
François-Xavier Le Dimet, Victor Petrovich Shutyaev, Jiafeng Wang, Mu Mu (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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The soil water movement model governed by the initial-boundary value problem for a quasilinear 1-D parabolic equation with nonlinear coefficients is considered. The generalized statement of the problem is formulated. The solvability of the problem is proved in a certain class of functional spaces. The data assimilation problem for this model is analysed. The numerical results are presented.
Stanislav Antontsev, Jesus Ildefonso Díaz, Serguei I. Shmarev (1995)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Carlos Escudero, Filippo Gazzola, Robert Hakl, Ireneo Peral, Pedro José Torres (2015)
Mathematica Bohemica
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We study a higher order parabolic partial differential equation that arises in the context of condensed matter physics. It is a fourth order semilinear equation which nonlinearity is the determinant of the Hessian matrix of the solution. We consider this model in a bounded domain of the real plane and study its stationary solutions both when the geometry of this domain is arbitrary and when it is the unit ball and the solution is radially symmetric. We also consider the initial-boundary...