Reaction diffusion equations (6ECTS)

Dr. Evangelos Latos

Mi. 12:00 - 13:30 in A5,6 C115

Tutorial:  Mi. 13:45-15:15 in  A5,6 C115

Content: This is a course focused on the qualitative properties of reaction diffusion parabolic problems. We will consider simple nonlinear, in the reaction term, parabolic problems and by studying them we will go through the main properties of the solutions. More specifically, we will examine notions like: well posedness, local and global-in-time solutions, stability and blow-up.

In many parabolic problems there exist global solutions (in particular, stationary solutions). On the other hand, it is known that a solution may cease to exist in a finite time as a consequence of its L^\infty norm becoming unbounded: The solution blows up. Both global and blowing- up solutions may be very unstable and they may exhibit a rather complicated asymptotic behavior. 

 

Language: English.

Prerequisites: Linear algebra I, Analysis I,II, basic knowledge of differential equations.

Reference:

Pavol Quittner, Philippe Souplet, Superlinear parabolic problems: blow-up, global existence and steady states, Birkhäuser Verlag Basel - Boston - Berlin, 2007. 

Jerrold Bebernes, David Eberly, Mathematical Problems from Combustion Theory, Springer-Verlag New York, 1989.

Michel Chipot, Elements of Nonlinear Analysis (Birkhäuser Advanced Texts) Birkhäuser Basel, 2000.

Samarskii, A.A. and Galaktionov, V. and Kurdyumov, S. and Mikhailov, A.P. and Grinfeld, M., Blow-Up in Quasilinear Parabolic Equations, De Gruyter Expositions in Mathematics, 1995.

Lawrence C. Evans, Partial Differential Equations, Second Edition, AMS, 2010.