Displaying similar documents to “Summability of the solutions to nonlinear parabolic equations with measure data.”

Existence of explosive solutions to some nonlinear parabolic Itô equations

Pao-Liu Chow (2015)

Banach Center Publications


The paper is concerned with the problem of existence of explosive solutions for a class of nonlinear parabolic Itô equations. Under some sufficient conditions on the initial state and the coefficients, it is proven by the method of auxiliary functionals that there exist explosive solutions with positive probability. The main results are presented in Theorems 3.1 and 3.2 under different sets of conditions. An example is given to illustrate some application of the second theorem. ...

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

Dmitry Portnyagin (2008)

Applicationes Mathematicae


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.

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

Ji Liu, Jia-Shan Zheng (2015)

Czechoslovak Mathematical Journal


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...

Summability of semicontinuous supersolutions to a quasilinear parabolic equation

Juha Kinnunen, Peter Lindqvist (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze


We study the so-called p -superparabolic functions, which are defined as lower semicontinuous supersolutions of a quasilinear parabolic equation. In the linear case, when p = 2 , we have supercaloric functions and the heat equation. We show that the p -superparabolic functions have a spatial Sobolev gradient and a sharp summability exponent is given.