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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 value problem...

Extension of a result of Ladyženskaja and Uralceva concerning second-order parabolic equations of arbitrary order

Wolf von Wahl (1983)

Annales Polonici Mathematici

Extrapolation Methods for Dynamic Partial Differential Equations.

E. Türkei (1977/1978)

Numerische Mathematik

Familles de convexes invariantes et équations de diffusion-réaction

Christine Reder (1982)

Annales de l'institut Fourier

Pour localiser la solution d’un système de diffusion-réaction, il suffit de construire une famille de convexes $(K_{t})_{t \geq 0}$ , invariante par rapport au champ de vecteurs associé à ce système; la solution est alors incluse dans $K_{t}$ à l’instant $t$ dès qu’elle est contenue dans $K_{0}$ à l’instant zéro. Les fonctions d’appui associées à de telles familles de convexes sont solutions d’un système différentiel, mais celui-ci peut également engendrer des familles non invariantes.

Finite element analysis of a system of quasi-parabolic partial differential equations

Jozef Brilla (1974)

Acta Universitatis Carolinae. Mathematica et Physica

Fourth-order partial differential equations for effective image denoising.

Kim, Seongjai, Lim, Hyeona (2009)

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

Gain of regularity for equations of KdV type

W. Craig, T. Kappeler, W. Strauss (1992)

Annales de l'I.H.P. Analyse non linéaire

Galerkin approximations for nonlinear evolution inclusions

Shouchuan Hu, Nikolaos S. Papageorgiou (1994)

Commentationes Mathematicae Universitatis Carolinae

In this paper we study the convergence properties of the Galerkin approximations to a nonlinear, nonautonomous evolution inclusion and use them to determine the structural properties of the solution set and establish the existence of periodic solutions. An example of a multivalued parabolic p.d.ei̇s also worked out in detail.

Global Attractor for a Class of Parabolic Equations with Infinite Delay

Cung The Anh, Le Van Hieu, Dang Thi Phuong Thanh (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

We prove the existence of a compact connected global attractor for a class of abstract semilinear parabolic equations with infinite delay.

Global existence for a Riccati equation arising in a boundary control problem for distributed parameters

Franco Flandoli (1982)

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

Si prova resistenza globale della soluzione di una equazione di Riccati collegata alla sintesi di un problema di controllo ottimale. Il problema considerato rappresenta la versione astratta di alcuni problemi governati da equazioni paraboliche con il controllo sulla frontiera.

Global Instability and Essential Spectrum in Semilinear Evolution Equations.

J. Solà-Morales (1986)

Mathematische Annalen

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