Displaying similar documents to “Quasilinear parabolic equations”

On the parabolic-elliptic limit of the doubly parabolic Keller-Segel system modelling chemotaxis

Piotr Biler, Lorenzo Brandolese (2009)

Studia Mathematica

Similarity:

We establish new results on convergence, in strong topologies, of solutions of the parabolic-parabolic Keller-Segel system in the plane to the corresponding solutions of the parabolic-elliptic model, as a physical parameter goes to zero. Our main tools are suitable space-time estimates, implying the global existence of slowly decaying (in general, nonintegrable) solutions for these models, under a natural smallness assumption.

Full regularity of bounded solutions to nondiagonal parabolic systems of two equations

Dmitry Portnyagin (2008)

Applicationes Mathematicae

Similarity:

Hölder continuity and, basing on this, full regularity and global existence of weak solutions is studied for a general nondiagonal parabolic system of nonlinear differential equations with the matrix of coefficients satisfying special structure conditions and depending on the unknowns. A technique based on estimating a certain function of unknowns is employed to this end.

The quasilinear parabolic kirchhoff equation

Łukasz Dawidowski (2017)

Open Mathematics

Similarity:

In this paper the existence of solution of a quasilinear generalized Kirchhoff equation with initial – boundary conditions of Dirichlet type will be studied using the Leray – Schauder principle.

New a priori estimates for nondiagonal strongly nonlinear parabolic systems

Arina Arkhipova (2008)

Banach Center Publications

Similarity:

We consider nondiagonal elliptic and parabolic systems of equations with quadratic nonlinearities in the gradient. We discuss a new description of regular points of solutions of such systems. For a class of strongly nonlinear parabolic systems, we estimate locally the Hölder norm of a solution. Instead of smallness of the oscillation, we assume local smallness of the Campanato seminorm of the solution under consideration. Theorems about quasireverse Hölder inequalities proved by the...