Displaying similar documents to “On blowup of a solution to a Sobolev-type equation with a nonlocal source.”

Blow-up versus global existence of solutions to aggregation equations

Grzegorz Karch, Kanako Suzuki (2011)

Applicationes Mathematicae

Similarity:

A class of nonlinear viscous transport equations describing aggregation phenomena in biology is considered. General conditions on an interaction potential are obtained which lead either to the existence or to the nonexistence of global-in-time solutions.

Integro-differential systems with variable exponents of nonlinearity

Oleh Buhrii, Nataliya Buhrii (2017)

Open Mathematics

Similarity:

Some nonlinear integro-differential equations of fourth order with variable exponents of the nonlinearity are considered. The initial-boundary value problem for these equations is investigated and the existence theorem for the problem is proved.

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

Ji Liu, Jia-Shan Zheng (2015)

Czechoslovak Mathematical Journal

Similarity:

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...

Global in time solvability of the initial boundary value problem for some nonlinear dissipative evolution equations

Yoshihiro Shibata (1993)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

The global in time solvability of the one-dimensional nonlinear equations of thermoelasticity, equations of viscoelasticity and nonlinear wave equations in several space dimensions with some boundary dissipation is discussed. The blow up of the solutions which might be possible even for small data is excluded by allowing for a certain dissipative mechanism.