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Displaying 21 – 35 of 35

Global existence of smooth solutions for the Vlasov-Fokker-Planck equation in $1$ and $2$ space dimensions

Pierre Degond (1986)

Annales scientifiques de l'École Normale Supérieure

Global existence versus blow up for some models of interacting particles

Piotr Biler, Lorenzo Brandolese (2006)

Colloquium Mathematicae

We study the global existence and space-time asymptotics of solutions for a class of nonlocal parabolic semilinear equations. Our models include the Nernst-Planck and Debye-Hückel drift-diffusion systems as well as parabolic-elliptic systems of chemotaxis. In the case of a model of self-gravitating particles, we also give a result on the finite time blow up of solutions with localized and oscillating complex-valued initial data, using a method due to S. Montgomery-Smith.

Global Instability and Essential Spectrum in Semilinear Evolution Equations.

J. Solà-Morales (1986)

Mathematische Annalen

Global $L^{\infty}$ bounds for a class of quasilinear parabolic equations.

Horn, Werner (2002)

Southwest Journal of Pure and Applied Mathematics [electronic only]

Global Regularity of Solutions of Nonlinear Second Order Elliptic and Parabolic Differential Equations.

Gary M. Liebermann (1986)

Mathematische Zeitschrift

Global solution to a generalized nonisothermal Ginzburg-Landau system

Nesrine Fterich (2010)

Applications of Mathematics

The article deals with a nonlinear generalized Ginzburg-Landau (Allen-Cahn) system of PDEs accounting for nonisothermal phase transition phenomena which was recently derived by A. Miranville and G. Schimperna: Nonisothermal phase separation based on a microforce balance, Discrete Contin. Dyn. Syst., Ser. B, 5 (2005), 753–768. The existence of solutions to a related Neumann-Robin problem is established in an $N \leq 3$ -dimensional space setting. A fixed point procedure guarantees the existence of solutions...

Global solutions of nonlinear parabolic equations

Matania Ben-Artzi (1992)

Journées équations aux dérivées partielles

Global solutions of semilinear heat equations in Hilbert spaces.

Iancu, G.Mihai, Wong, M.W. (1996)

Abstract and Applied Analysis

Global solutions via partial information and the Cahn-Hilliard equation

Jan Cholewa, Tomasz Dłotko (1996)

Banach Center Publications

Global solutions of semilinear parabolic equations are studied in the case when some weak a priori estimate for solutions of the problem under consideration is already known. The focus is on the rapid growth of the nonlinear term for which existence of the semigroup and certain dynamic properties of the considered system can be justified. Examples including the famous Cahn-Hilliard equation are finally discussed.

Global solvability in the parabolic-elliptic chemotaxis system with singular sensitivity and logistic source

Xiangdong Zhao (2024)

Czechoslovak Mathematical Journal

We study the chemotaxis system with singular sensitivity and logistic-type source: $u_{t} = Δ u - χ \nabla \cdot (u \nabla v / v) + r u - μ u^{k}$ , $0 = Δ v - v + u$ under the non-flux boundary conditions in a smooth bounded domain $Ω \subset ℝ^{n}$ , $χ, r, μ > 0$ , $k > 1$ and $n \geq 1$ . It is shown with $k \in (1, 2)$ that the system possesses a global generalized solution for $n \geq 2$ which is bounded when $χ > 0$ is suitably small related to $r > 0$ and the initial datum is properly small, and a global bounded classical solution for $n = 1$ .

Global well-posedness for the 2D quasi-geostrophic equation in a critical Besov space.

Stefanov, Atanas (2007)

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

Global φ-attractor for a modified 3D Bénard system on channel-like domains

O.V. Kapustyan, A.V. Pankov (2014)

Nonautonomous Dynamical Systems

In this paper we prove the existence of a global φ-attractor in the weak topology of the natural phase space for the family of multi-valued processes generated by solutions of a nonautonomous modified 3D Bénard system in unbounded domains for which Poincaré inequality takes place.

Currently displaying 21 – 35 of 35