Displaying similar documents to “The Cauchy problem and self-similar solutions for a nonlinear parabolic equation”

Existence of solutions for a model of self-gravitating particles with external potential

Andrzej Raczyński (2004)

Banach Center Publications

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We study the existence of solutions to a nonlinear parabolic equation describing the temporal evolution of a cloud of self-gravitating particles with a given external potential. The initial data are in spaces of (generalized) pseudomeasures. We prove existence of local and global-in-time solutions, and also a kind of stability of global solutions.

Existence of explosive solutions to some nonlinear parabolic Itô equations

Pao-Liu Chow (2015)

Banach Center Publications

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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. ...

Existence of solutions for infinite systems of parabolic equations with functional dependence

Anna Pudełko (2005)

Annales Polonici Mathematici

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The Cauchy problem for an infinite system of parabolic type equations is studied. General operators of parabolic type of second order with variable coefficients are considered and the system is weakly coupled. We prove the existence and uniqueness of a bounded solution under Carathéodory type conditions and its differentiability, as well as the existence and uniqueness in the class of functions satisfying a natural growth condition. Both results are obtained by the fixed point method. ...

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...

A note on the paper of Y. Naito

Piotr Biler (2006)

Banach Center Publications

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This note contains some remarks on the paper of Y. Naito concerning the parabolic system of chemotaxis and published in this volume.

Analyticity of the maximal solution of an abstract parabolic equation

Alessandra Lunardi (1981)

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

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Studia l’analiticità della soluzione massimale di una equazione parabolica astratta in spazi di Banach.

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

Piotr Biler, Lorenzo Brandolese (2009)

Studia Mathematica

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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.