Displaying similar documents to “Non-simultaneous blow-up for a semilinear parabolic system with nonlinear memory.”

Remarks on blow up time for solutions of a nonlinear diffusion system with time dependent coefficients

Marras, M. (2011)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 35K55, 35K60. We investigate the blow-up of the solutions to a nonlinear parabolic system with Robin boundary conditions and time dependent coefficients. We derive sufficient conditions on the nonlinearities and the initial data in order to obtain explicit lower and upper bounds for the blow up time t*.

Instantaneous shrinking of the support for solutions to certain parabolic equations and systems

Anatolii S. Kalashnikov (1997)

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

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The paper contains conditions ensuring instantaneous shrinking of the support for solutions to semilinear parabolic equations with compactly supported coefficients of nonlinear terms and reaction-diffusion systems.

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...

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. ...