Displaying similar documents to “Existence and asymptotics of solutions of the Debye-Nernst-Planck system in ℝ²”

On radially symmetric solutions of some chemotaxis system

Robert Stańczy (2009)

Banach Center Publications

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This paper contains some results concerning self-similar radial solutions for some system of chemotaxis. This kind of solutions describe asymptotic profiles of arbitrary solutions with small mass. Our approach is based on a fixed point analysis for an appropriate integral operator acting on a suitably defined convex subset of some cone in the space of bounded and continuous functions.

Existence of solutions for a model of self-gravitating particles with external potential

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.

Growth and accretion of mass in an astrophysical model, II

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.

On some parabolic-elliptic system with self-similar pressure term

Robert Stańczy (2006)

Banach Center Publications

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A priori estimates for solutions of a system describing the interaction of gravitationally attracting particles with a self-similar pressure term are proved. The presented theory covers the case of the model with diffusions that obey either Fermi-Dirac statistics or a polytropic one.

Spherically symmetric solutions to a model for interface motion by interface diffusion

Zhu, Peicheng

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The existence of spherically symmetric solutions is proved for a new phase-field model that describes the motion of an interface in an elastically deformable solid, here the motion is driven by configurational forces. The model is an elliptic-parabolic coupled system which consists of a linear elasticity system and a non-linear evolution equation of the order parameter. The non-linear equation is non-uniformly parabolic and is of fourth order. One typical application is sintering. ...

Existence and nonexistence of solutions for a model of gravitational interaction of particles, II

Piotr Biler, Danielle Hilhorst, Tadeusz Nadzieja (1994)

Colloquium Mathematicae

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We study the existence and nonexistence in the large of radial solutions to a parabolic-elliptic system with natural (no-flux) boundary conditions describing the gravitational interaction of particles. The blow-up of solutions defined in the n-dimensional ball with large initial data is connected with the nonexistence of radial stationary solutions with a large mass.

Existence results for a fourth order partial differential equation arising in condensed matter physics

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...

Weak Solutions for a Fourth Order Degenerate Parabolic Equation

Changchun Liu, Jinyong Guo (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

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We consider an initial-boundary value problem for a fourth order degenerate parabolic equation. Under some assumptions on the initial value, we establish the existence of weak solutions by the discrete-time method. The asymptotic behavior and the finite speed of propagation of perturbations of solutions are also discussed.

The Cauchy problem and self-similar solutions for a nonlinear parabolic equation

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.

Fundamental solutions and asymptotic behaviour for the p-Laplacian equation.

Soshana Kamin, Juan Luis Vázquez (1988)

Revista Matemática Iberoamericana

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We establish the uniqueness of fundamental solutions to the p-Laplacian equation ut = div (|Du|p-2 Du),   p > 2, defined for x ∈ RN, 0 < t < T. We derive from this result the asymptotic behavoir of nonnegative solutions with finite mass, i.e., such that u(*,t) ∈ L1(RN). Our methods also apply to the porous medium equation ut...