Exact Traveling Wave Solutions Of One Dimensional Parabolic Parabolic Models Of Chemotaxis
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Author | : Maria Vladimirovna Shubina |
Publisher | : |
Total Pages | : 0 |
Release | : 2020 |
Genre | : Electronic books |
ISBN | : |
In this chapter we consider several different parabolic-parabolic systems of chemotaxis which depend on time and one space coordinate. For these systems we obtain the exact analytical solutions in terms of traveling wave variables. Not all of these solutions are acceptable for biological interpretation, but there are solutions that require detailed analysis. We find this interesting, since chemotaxis is present in the continuous mathematical models of cancer growth and invasion (Anderson, Chaplain, Lolas, et al.) which are described by the systems of reaction,Äìdiffusion-taxis partial differential equations, and the obtaining of exact solutions to these systems seems to be a very interesting task, and a more detailed analysis is possible in a future study.
Author | : A. I. Volpert |
Publisher | : American Mathematical Soc. |
Total Pages | : 474 |
Release | : |
Genre | : Mathematics |
ISBN | : 9780821897577 |
The theory of travelling waves described by parabolic equations and systems is a rapidly developing branch of modern mathematics. This book presents a general picture of current results about wave solutions of parabolic systems, their existence, stability, and bifurcations. With introductory material accessible to non-mathematicians and a nearly complete bibliography of about 500 references, this book is an excellent resource on the subject.
Author | : Lyudmila Alexeyeva |
Publisher | : BoD – Books on Demand |
Total Pages | : 149 |
Release | : 2020-12-09 |
Genre | : |
ISBN | : 1838800719 |
The main content of this book is related to construction of analytical solutions of differential equations and systems of mathematical physics, to development of analytical methods for solving boundary value problems for such equations and the study of properties of their solutions. A wide class of equations (elliptic, parabolic, and hyperbolic) is considered here, on the basis of which complex wave processes in biological and physical media can be simulated.The method of generalized functions presented in the book for solving boundary value problems of mathematical physics is universal for constructing solutions of boundary value problems for systems of linear differential equations with constant coefficients of any type. In the last sections of the book, the issues of calculating functions based on Padé approximations, binomial expansions, and fractal representations are considered. The book is intended for specialists in the field of mathematical and theoretical physics, mechanics and biophysics, students of mechanics, mathematics, physics and biology departments of higher educational institutions.
Author | : Aĭzik Isaakovich Volʹpert |
Publisher | : American Mathematical Society(RI) |
Total Pages | : 448 |
Release | : 1994 |
Genre | : Chemical kinetics |
ISBN | : 9780821846094 |
The theory of traveling waves described by parabolic equations and systems is a rapidly developing branch of modern mathematics. This book presents a general picture of current results about wave solutions of parabolic systems, their existence, stability, and bifurcations. The main part of the book contains original approaches developed by the authors. Among these are a description of the long-term behavior of the solutions by systems of waves; construction of rotations of vector fields for noncompact operators describing wave solutions; a proof of the existence of waves by the Leray-Schauder method; local, global, and nonlinear stability analyses for some classes of systems; and a determination of the wave velocity by the minimax method and the method of successive approximations. The authors show that wide classes of reaction-diffusion systems can be reduced to so-called monotone and locally monotone systems. This fundamental result allows them to apply the theory to combustion and chemical kinetics. With introductory material accessible to nonmathematicians and a nearly complete bibliography of about 500 references, this book is an excellent resource on the subject.
Author | : Patrick Shawn Hagan |
Publisher | : |
Total Pages | : 678 |
Release | : 1979 |
Genre | : |
ISBN | : |
Author | : Michael D. Collins |
Publisher | : Springer Nature |
Total Pages | : 135 |
Release | : 2019-11-04 |
Genre | : Science |
ISBN | : 1493999346 |
This book introduces parabolic wave equations, their key methods of numerical solution, and applications in seismology and ocean acoustics. The parabolic equation method provides an appealing combination of accuracy and efficiency for many nonseparable wave propagation problems in geophysics. While the parabolic equation method was pioneered in the 1940s by Leontovich and Fock who applied it to radio wave propagation in the atmosphere, it thrived in the 1970s due to its usefulness in seismology and ocean acoustics. The book covers progress made following the parabolic equation’s ascendancy in geophysics. It begins with the necessary preliminaries on the elliptic wave equation and its analysis from which the parabolic wave equation is derived and introduced. Subsequently, the authors demonstrate the use of rational approximation techniques, the Padé solution in particular, to find numerical solutions to the energy-conserving parabolic equation, three-dimensional parabolic equations, and horizontal wave equations. The rest of the book demonstrates applications to seismology, ocean acoustics, and beyond, with coverage of elastic waves, sloping interfaces and boundaries, acousto-gravity waves, and waves in poro-elastic media. Overall, it will be of use to students and researchers in wave propagation, ocean acoustics, geophysical sciences and more.
Author | : Dirk Horstmann |
Publisher | : |
Total Pages | : 21 |
Release | : 2001 |
Genre | : Boundary value problems |
ISBN | : |
Abstract: "In this paper we study the existence of one and multidimensional traveling wave solutions for chemotaxis or so-called Keller-Segel models. We present a constructive approach to give modelers a choice of sensitivity, production and decay functionals at hand."
Author | : V. Capasso (Ed) |
Publisher | : Società Editrice Esculapio |
Total Pages | : 659 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 8874880553 |
Author | : Benoît Perthame |
Publisher | : Springer Science & Business Media |
Total Pages | : 206 |
Release | : 2006-12-14 |
Genre | : Science |
ISBN | : 3764378425 |
This book presents models written as partial differential equations and originating from various questions in population biology, such as physiologically structured equations, adaptive dynamics, and bacterial movement. Its purpose is to derive appropriate mathematical tools and qualitative properties of the solutions. The book further contains many original PDE problems originating in biosciences.
Author | : |
Publisher | : |
Total Pages | : 1852 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : |