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On the Caginalp system with dynamic boundary conditions and singular potentials

Laurence Cherfils, Alain Miranville (2009)

Applications of Mathematics

This article is devoted to the study of the Caginalp phase field system with dynamic boundary conditions and singular potentials. We first show that, for initial data in H 2 , the solutions are strictly separated from the singularities of the potential. This turns out to be our main argument in the proof of the existence and uniqueness of solutions. We then prove the existence of global attractors. In the last part of the article, we adapt well-known results concerning the Łojasiewicz inequality in...

On the Convective Cahn-Hilliard Equation

Changchun Liu (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

The author studies the convective Cahn-Hilliard equation. Some results on the existence of classical solutions and asymptotic behavior of solutions are established. The instability of the traveling waves is also discussed.

On the eigenfunction expansion method for semilinear dissipative equations in bounded domains and the Kuramoto-Sivashinsky equation in a ball

V. V. Varlamov (2001)

Studia Mathematica

Presented herein is a method of constructing solutions of semilinear dissipative evolution equations in bounded domains. For small initial data this approach permits one to represent the solution in the form of an eigenfunction expansion series and to calculate the higher-order long-time asymptotics. It is applied to the spatially 3D Kuramoto-Sivashinsky equation in the unit ball B in the linearly stable case. A global-in-time mild solution is constructed in the space C ⁰ ( [ 0 , ∞ ) , H ₀ s ( B ) ) , s < 2, and the uniqueness...

On the existence and regularity of the solutions to the incompressible Navier-Stokes equations in presence of mass diffusion

Rodolfo Salvi (2008)

Banach Center Publications

This paper is devoted to the study of the incompressible Navier-Stokes equations with mass diffusion in a bounded domain in R³ with C³ boundary. We prove the existence of weak solutions, in the large, and the behavior of the solutions as the diffusion parameter λ → 0. Moreover, the existence of L²-strong solution, in the small, and in the large for small data, is proved. Asymptotic regularity (the regularity after a finite period) of a weak solution is studied. Finally, using the Dore-Venni theory,...

On the G -convergence of Morrey operators

Maria Rosaria Formica, Carlo Sbordone (2003)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Following Morrey [14] we associate to any measurable symmetric 2 × 2 matrix valued function A ⁢ x such that ξ 2 K ≤ A ⁢ x ⁢ ξ , ξ ≤ K ⁢ ξ 2 ⁢ a.e. ⁢ x ∈ Ω , ∀ ξ ∈ R 2 , Ω ∈ R 2 ...

Currently displaying 81 – 100 of 144