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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 and nonexistence of solutions for a model of gravitational interaction of particles, III

Piotr Biler (1995)

Colloquium Mathematicae

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

Piotr Biler, Tadeusz Nadzieja (1993)

Colloquium Mathematicae

We study the existence of stationary and evolution solutions to a parabolic-elliptic system with natural (no-flux) boundary conditions describing the gravitational interaction of particles.

Existence and nonexistence results for a class of linear and semilinear parabolic equations related to some Caffarelli-Kohn-Nirenberg inequalities

Boumediene Abdellaoui, Eduardo Colorado, Ireneo Peral (2004)

Journal of the European Mathematical Society

In this work we study the problem $u_{t} {- div (| x |}^{- 2 γ} \nabla u) = λ \frac{u^{α}}{{| x |}^{2 (γ + 1)}} + f$ in $Ω \times (0, T)$ , $u \geq 0$ in $Ω \times (0, T)$ , $u = 0$ on $\partial Ω \times (0, T)$ , $u (x, 0) = u_{0} (x)$ in $Ω$ , $Ω \subset ℝ^{N}$ $(N \geq 2)$ is a bounded regular domain such that $0 \in Ω$ , $λ > 0$ , $α > 0$ , $- \infty < γ < (N - 2) / 2$ , $f$ and $u_{0}$ are positive functions such...

Existence and non-existence results for a nonlinear heat equation.

Celik, Canan (2007)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence and nonexistence results for reaction-diffusion equations in product of cones

Abdallah Hamidi, Gennady Laptev (2003)

Open Mathematics

Problems of existence and nonexistence of global nontrivial solutions to quasilinear evolution differential inequalities in a product of cones are investigated. The proofs of the nonexistence results are based on the test-function method developed, for the case of the whole space, by Mitidieri, Pohozaev, Tesei and Véron. The existence result is established using the method of supersolutions.

Existence and perturbation of principal eigenvalues for a periodic-parabolic problem.

Daners, Daniel (2000)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence and properties of the Green function for a class of degenerate parabolic equations.

José C. Fernandes, Bruno Franchi (1996)

Revista Matemática Iberoamericana

It is known that degenerate parabolic equations exhibit somehow different phenomena when we compare them with their elliptic counterparts. Thus, the problem of existence and properties of the Green function for degenerate parabolic boundary value problems is not completely solved, even after the contributions of [GN] and [GW4], in the sense that the existence problem is still open, even if the a priori estimates proved in [GN] will be crucial in our approach (...).

Existence and regularity for semilinear parabolic evolution equations

Herbert Amann (1984)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Existence and regularity of a global attractor for doubly nonlinear parabolic equations.

El Hachimi, Abderrahmane, El Ouardi, Hamid (2002)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence and regularity of optimal solution for a dead oil isotherm problem.

Sidi Ammi, Moulay Rchid, Torres, Delfim F.M. (2007)

APPS. Applied Sciences

Existence and regularity results for the gradient flow for $p$ -harmonic maps.

Misawa, Masashi (1998)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence and stability of asymptotically oscillatory double pulses.

J.C. Alexander, C.K.R.T. Jones (1994)

Journal für die reine und angewandte Mathematik

Existence and stability of periodic solutions for a nonlocal evolution population problem.

Maurizio Badii (2005)

RACSAM

The theory of maximal monotone operators is applied to prove the existence of weak periodic solutions for a nonlinear nonlocal problem. The stability of these solutions is a consequence of the Lipschitz continuous assumption on the diffusivity matrix and the death rate.

Existence and stability theorems for abstract parabolic equations, and some of their applications

Gerhard Ströhmer, Wojciech Zajączkowski (1996)

Banach Center Publications

For a class of semi-abstract evolution equations for sections on vector bundles on a three-dimensional compact manifold we prove that for initial values with certain symmetries strong solutions exist for all times. In case these solutions become small after some time, strong solutions exist also for small perturbations of these initial values. Many systems from fluid mechanics are included in this class.

Existence and uniqueness for one-phase Stefan problems of nonclassical heat equations with temperature boundary condition at a fixed face.

Briozzo, Adriana C., Tarzia, Domingo A. (2006)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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