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On hyperbolic partial differential equations in Banach spaces

Bogdan Rzepecki (1986)

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

Viene dimostrata l'esistenza di soluzioni del problema di Darboux per l'equazione iperbolica z x y ′′ = f ( x , y , z , Z x , z y ) sul planiquarto x 0 , y 0 . Qui, f è una funzione continua, con valori in uno spazio Banach che soddisfano alcune condizioni di regolarità espresse in termini della misura di non-compattezza α .

On hypoellipticity in 𝒢 .

Nedeljkov, M., Pilipović, S. (2002)

Bulletin. Classe des Sciences Mathématiques et Naturelles. Sciences Mathématiques

On hypoellipticity in g

M. Nedeljkov, S. Pilipović (2002)

Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques

On identification of critical curves

Jaroslav Haslinger, Václav Horák (1990)

Aplikace matematiky

The paper deals with the problem of finding a curve, going through the interior of the domain Ω , accross which the flux u / n , where u is the solution of a mixed elliptic boundary value problem solved in Ω , attains its maximum.

On inertial manifolds for reaction-diffusion equations on genuinely high-dimensional thin domains

M. Prizzi, K. P. Rybakowski (2003)

Studia Mathematica

We study a family of semilinear reaction-diffusion equations on spatial domains Ω ε , ε > 0, in l lying close to a k-dimensional submanifold ℳ of l . As ε → 0⁺, the domains collapse onto (a subset of) ℳ. As proved in [15], the above family has a limit equation, which is an abstract semilinear parabolic equation defined on a certain limit phase space denoted by H ¹ s ( Ω ) . The definition of H ¹ s ( Ω ) , given in the above paper, is very abstract. One of the objectives of this paper is to give more manageable characterizations...

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