Displaying similar documents to “Highly degenerate quasilinear parabolic systems”

Linear parabolic problems involving measures.

Herbert Amann (2001)

RACSAM

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Desarrollamos una teoría general para la resolución de ecuaciones lineales de evolución de la forma ü + Au = μ sobre R+, donde -A es el generador infinitesimal de un semigrupo analítico fuertemente continuo y μ es una medida de Radón con valores en un espacio de Banach. Utilizamos la teoría de interpolación-extrapolación de espacios y el teorema de representación de Riesz para tales medidas. Los resultados abstractos son ilustrados mediante aplicaciones...

Boundedness in a quasilinear parabolic-parabolic chemotaxis system with nonlinear logistic source

Ji Liu, Jia-Shan Zheng (2015)

Czechoslovak Mathematical Journal

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We study a quasilinear parabolic-parabolic chemotaxis system with nonlinear logistic source, under homogeneous Neumann boundary conditions in a smooth bounded domain. By establishing proper a priori estimates we prove that, with both the diffusion function and the chemotaxis sensitivity function being positive, the corresponding initial boundary value problem admits a unique global classical solution which is uniformly bounded. The result of this paper is a generalization of that of...

Stabilization in degenerate parabolic equations in divergence form and application to chemotaxis systems

Sachiko Ishida, Tomomi Yokota (2023)

Archivum Mathematicum

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This paper presents a stabilization result for weak solutions of degenerate parabolic equations in divergence form. More precisely, the result asserts that the global-in-time weak solution converges to the average of the initial data in some topology as time goes to infinity. It is also shown that the result can be applied to a degenerate parabolic-elliptic Keller-Segel system.

Abstract methods in differential equations.

Herbert Amann (2003)

RACSAM

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This is an expanded version, enriched by references, of my inaugural speech held on November 7, 2001 at the Real Academia de Ciencas Exactas, Físicas y Naturales in Madrid. It explains in a nontechnical way, accessible to a general scientific community, some of the motivation and basic ideas of my research of the last twenty years on a functional-analytical approach to nonlinear parabolic problems.

Maximal regularity for abstract parabolic problems with inhomogeneous boundary data in  L p -spaces

Jan Prüss (2002)

Mathematica Bohemica

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Several abstract model problems of elliptic and parabolic type with inhomogeneous initial and boundary data are discussed. By means of a variant of the Dore-Venni theorem, real and complex interpolation, and trace theorems, optimal L p -regularity is shown. By means of this purely operator theoretic approach, classical results on L p -regularity of the diffusion equation with inhomogeneous Dirichlet or Neumann or Robin condition are recovered. An application to a dynamic boundary value problem...