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Time and space Sobolev regularity of solutions to homogeneous parabolic equations

Gabriella Di Blasio (1998)

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

We give necessary and sufficient conditions on the initial data such that the solutions of parabolic equations have a prescribed Sobolev regularity in time and space.

Time asymptotic description of an abstract Cauchy problem solution and application to transport equation

Boulbeba Abdelmoumen, Omar Jedidi, Aref Jeribi (2014)

Applications of Mathematics

In this paper, we study the time asymptotic behavior of the solution to an abstract Cauchy problem on Banach spaces without restriction on the initial data. The abstract results are then applied to the study of the time asymptotic behavior of solutions of an one-dimensional transport equation with boundary conditions in L 1 -space arising in growing cell populations and originally introduced by M. Rotenberg, J. Theoret. Biol. 103 (1983), 181–199.

Time delays in proliferation and apoptosis for solid avascular tumour

Urszula Foryś, Mikhail Kolev (2003)

Banach Center Publications

The role of time delays in solid avascular tumour growth is considered. The model is formulated in terms of a reaction-diffusion equation and mass conservation law. Two main processes are taken into account-proliferation and apoptosis. We introduce time delay first in underlying apoptosis only and then in both processes. In the absence of necrosis the model reduces to one ordinary differential equation with one discrete delay which describes the changes of tumour radius. Basic properties of the...

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