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Global existence of solutions to a chemotaxis system with volume filling effect

Tomasz Cieślak (2008)

Colloquium Mathematicae

A system of quasilinear parabolic equations modelling chemotaxis and taking into account the volume filling effect is studied under no-flux boundary conditions. The resulting system is non-uniformly parabolic. A Lyapunov functional for the system is constructed. The proof of existence and uniqueness of regular global-in-time solutions is given in cases when either the Lyapunov functional is bounded from below or chemotactic forces are suitably weakened. In the first case solutions are uniformly...

Global Schauder estimates for a class of degenerate Kolmogorov equations

Enrico Priola (2009)

Studia Mathematica

We consider a class of possibly degenerate second order elliptic operators on ℝⁿ. This class includes hypoelliptic Ornstein-Uhlenbeck type operators having an additional first order term with unbounded coefficients. We establish global Schauder estimates in Hölder spaces both for elliptic equations and for parabolic Cauchy problems involving . The Hölder spaces in question are defined with respect to a possibly non-Euclidean metric related to the operator . Schauder estimates are deduced by sharp...

Global weak solutions for a degenerate parabolic system modelling a one-dimensional compressible miscible flow in porous media

Y. Amirat, A. Ziani (2004)

Bollettino dell'Unione Matematica Italiana

We show the solvability of a nonlinear degenerate parabolic system of two equations describing the displacement of one compressible fluid by another, completely miscible with the first, in a one-dimensional porous medium, neglecting the molecular diffusion. We use the technique of renormalised solutions for parabolic equations in the derivation of a priori estimates for viscosity type solutions. We pass to the limit, as the molecular diffusion coefficient tends to 0, on the parabolic system, owing...

Harnack estimates for weak supersolutions to nonlinear degenerate parabolic equations

Tuomo Kuusi (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In this work we prove both local and global Harnack estimates for weak supersolutions to second order nonlinear degenerate parabolic partial differential equations in divergence form. We reduce the proof to an analysis of so-called hot and cold alternatives, and use the expansion of positivity together with a parabolic type of covering argument. Our proof uses only the properties of weak supersolutions. In particular, no comparison to weak solutions is needed.

Holomorphic subordinated semigroups

Adel Saddi (2002)

Commentationes Mathematicae Universitatis Carolinae

If ( e - t A ) t > 0 is a strongly continuous and contractive semigroup on a complex Banach space B , then - ( - A ) α , 0 < α < 1 , generates a holomorphic semigroup on B . This was proved by K. Yosida in [7]. Using similar techniques, we present a class H of Bernstein functions such that for all f ∈ H , the operator - f ( - A ) generates a holomorphic semigroup.

Homogenization of a three-phase composites of double-porosity type

Ahmed Boughammoura, Yousra Braham (2021)

Czechoslovak Mathematical Journal

In this work we consider a diffusion problem in a periodic composite having three phases: matrix, fibers and interphase. The heat conductivities of the medium vary periodically with a period of size ε β ( ε > 0 and β > 0 ) in the transverse directions of the fibers. In addition, we assume that the conductivity of the interphase material and the anisotropy contrast of the material in the fibers are of the same order ε 2 (the so-called double-porosity type scaling) while the matrix material has a conductivity of...

Homogenization of some nonlinear problems with specific dependence upon coordinates

P. Courilleau, S. Fabre, J. Mossino (2001)

Bollettino dell'Unione Matematica Italiana

Questo articolo considera una successione di equazioni differenziali a derivate parziali non lineari in forma di divergenza del tipo - div ⁢ Q ϵ ⁢ G ⁢ x , N ϵ ⁢ ∇ ⁡ u = f ϵ , in un dominio limitato Ω dello spazio n -dimensionale; Q ϵ = Q ϵ ⁢ x e N ϵ = N ϵ ⁢ x sono matrici con coefficenti limitati, N ϵ e è invertibile e la sua matrice inversa R ϵ ha anche coefficenti limitati. La non linearità è dovuta alla funzione G = G ⁢ x , ξ ; la condizione di crescita, la monotonicità e le ipotesi di coercitività sono modellate sul p -Laplaciano, 1 < p < ∞ , ed assicurano l'esistenza di una soluzione...

Currently displaying 181 – 200 of 417