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Parabolic equations in biologygrowth...

Perthame, Benoit.

Parabolic equations in biologygrowth, reaction, movement and diffusion /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Parabolic equations in biologyby Benoit Perthame.
其他題名:	growth, reaction, movement and diffusion /
作者:	Perthame, Benoit.
出版者:	Cham :Springer International Publishing :2015.
面頁冊數:	xii, 199 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer eBooks
標題:	Differential equations, Parabolic.
電子資源:	http://dx.doi.org/10.1007/978-3-319-19500-1
ISBN:	9783319195001$q(electronic bk.)

Parabolic equations in biologygrowth, reaction, movement and diffusion /
Perthame, Benoit.

Parabolic equations in biologygrowth, reaction, movement and diffusion /[electronic resource] :by Benoit Perthame. - Cham :Springer International Publishing :2015. - xii, 199 p. :ill. (some col.), digital ;24 cm. - Lecture notes on mathematical modelling in the life sciences,2193-4789. - Lecture notes on mathematical modelling in the life sciences..

1.Parabolic Equations in Biology -- 2.Relaxation, Perturbation and Entropy Methods -- 3.Weak Solutions of Parabolic Equations in whole Space -- 4.Traveling Waves -- 5.Spikes, Spots and Pulses -- 6.Blow-up and Extinction of Solutions -- 7.Linear Instability, Turing Instability and Pattern Formation -- 8.The Fokker-Planck Equation -- 9.From Jumps and Scattering to the Fokker-Planck Equation -- 10.Fast Reactions and the Stefan free Boundary Problem.

This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations. These are classical modeling tools for mathematical biology with applications to ecology and population dynamics, the neurosciences, enzymatic reactions, chemotaxis, invasion waves etc. The book presents these aspects from a mathematical perspective, with the aim of identifying those qualitative properties of the models that are relevant for biological applications. To do so, it uncovers the mechanisms at work behind Turing instability, pattern formation and invasion waves. This involves several mathematical tools, such as stability and instability analysis, blow-up in finite time, asymptotic methods and relative entropy properties. Given the content presented, the book is well suited as a textbook for master-level coursework.

ISBN: 9783319195001$q(electronic bk.)

Standard No.: 10.1007/978-3-319-19500-1doiSubjects--Topical Terms:

247280
Differential equations, Parabolic.

LC Class. No.: QA377

Dewey Class. No.: 515.3534

Parabolic equations in biologygrowth, reaction, movement and diffusion /
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100 1 $a Perthame, Benoit. $3 731705
245 1 0 $a Parabolic equations in biology $h [electronic resource] : $b growth, reaction, movement and diffusion / $c by Benoit Perthame.
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505 0 $a 1.Parabolic Equations in Biology -- 2.Relaxation, Perturbation and Entropy Methods -- 3.Weak Solutions of Parabolic Equations in whole Space -- 4.Traveling Waves -- 5.Spikes, Spots and Pulses -- 6.Blow-up and Extinction of Solutions -- 7.Linear Instability, Turing Instability and Pattern Formation -- 8.The Fokker-Planck Equation -- 9.From Jumps and Scattering to the Fokker-Planck Equation -- 10.Fast Reactions and the Stefan free Boundary Problem.
520 $a This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations. These are classical modeling tools for mathematical biology with applications to ecology and population dynamics, the neurosciences, enzymatic reactions, chemotaxis, invasion waves etc. The book presents these aspects from a mathematical perspective, with the aim of identifying those qualitative properties of the models that are relevant for biological applications. To do so, it uncovers the mechanisms at work behind Turing instability, pattern formation and invasion waves. This involves several mathematical tools, such as stability and instability analysis, blow-up in finite time, asymptotic methods and relative entropy properties. Given the content presented, the book is well suited as a textbook for master-level coursework.
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