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On one algorithm for solving the problem of source function reconstruction

Vyacheslav Maksimov (2010)

International Journal of Applied Mathematics and Computer Science

In the paper, the problem of source function reconstruction in a differential equation of the parabolic type is investigated. Using the semigroup representation of trajectories of dynamical systems, we build a finite-step iterative procedure for solving this problem. The algorithm originates from the theory of closed-loop control (the method of extremal shift). At every step of the algorithm, the sum of a quality criterion and a linear penalty term is minimized. This procedure is robust to perturbations...

On optimal L p regularity in evolution equations

Alessandra Lunardi (1999)

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

Using interpolation techniques we prove an optimal regularity theorem for the convolution u ⁢ t = ∫ 0 t T ⁢ t - s ⁢ f ⁢ s ⁢ d ⁢ s , where T ⁢ t is a strongly continuous semigroup in general Banach space. In the case of abstract parabolic problems – that is, when T ⁢ t is an analytic semigroup – it lets us recover in a unified way previous regularity results. It may be applied also to some non analytic semigroups, such as the realization of the Ornstein-Uhlenbeck semigroup in L p ⁢ R n , 1 < p < ∞ , in which case it yields new optimal regularity results in fractional...

On radially symmetric solutions of some chemotaxis system

Robert Stańczy (2009)

Banach Center Publications

This paper contains some results concerning self-similar radial solutions for some system of chemotaxis. This kind of solutions describe asymptotic profiles of arbitrary solutions with small mass. Our approach is based on a fixed point analysis for an appropriate integral operator acting on a suitably defined convex subset of some cone in the space of bounded and continuous functions.

On rates of propagation for Burgers’ equation

William Alan Day, Giuseppe Saccomandi (1998)

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

We give asymptotic formulae for the propagation of an initial disturbance of the Burgers’ equation.

On solutions of a perturbed fast diffusion equation

Ján Filo (1987)

Aplikace matematiky

The paper concerns the (local and global) existence, nonexistence, uniqueness and some properties of nonnegative solutions of a nonlinear density dependent diffusion equation with homogeneous Dirichlet boundary conditions.

On some free boundary problems for Navier-Stokes equations

Ewa Zadrzyńska (2005)

Banach Center Publications

In this survey we report on existence results for some free boundary problems for equations describing motions of both incompressible and compressible viscous fluids. We also present ways of controlling free boundaries in two cases: a) when the free boundary is governed by surface tension, b) when surface tension does not occur.

On some nonlocal systems containing a parabolic PDE and a first order ODE

Ádám Besenyei (2010)

Mathematica Bohemica

Two models of reaction-diffusion are presented: a non-Fickian diffusion model described by a system of a parabolic PDE and a first order ODE, further, porosity-mineralogy changes in porous medium which is modelled by a system consisting of an ODE, a parabolic and an elliptic equation. Existence of weak solutions is shown by the Schauder fixed point theorem combined with the theory of monotone type operators.

On some parabolic-elliptic system with self-similar pressure term

Robert Stańczy (2006)

Banach Center Publications

A priori estimates for solutions of a system describing the interaction of gravitationally attracting particles with a self-similar pressure term are proved. The presented theory covers the case of the model with diffusions that obey either Fermi-Dirac statistics or a polytropic one.

Currently displaying 121 – 140 of 336