bio  website  umpa.enslyon.fr/~serre 

location  Lyon, FRANCE  
age  60  
visits  member for  4 years, 7 months 
seen  3 hours ago  
stats  profile views  11,140 
My research activity is mainly in PDEs, with applications to Physics, especially in Fluid Dynamics. I have written a 2volume book on Conservation laws, and a book about the Hyperbolic IBVP (in collaboration with S. BenzoniGavage). I have edited in collaboration with S. Friedlander, a 4volume Handbook of Mathematical Fluid Dynamics.
I have a continuous interest in Matrix Analysis. I have written a Graduate Text about Matrices. The second edition has been released in November 2010.
3h

comment 
“C^0 estimate for solutions to $\Delta(u)+e^{u} \geq 0$”
This is not a special case. All the solutions $u$ are given by this formula, for a suitable holomorphic function $f$. 
8h

revised 
“C^0 estimate for solutions to $\Delta(u)+e^{u} \geq 0$”
added 204 characters in body 
11h

answered  “C^0 estimate for solutions to $\Delta(u)+e^{u} \geq 0$” 
Mar 28 
accepted  A “quadratic” triangular inequality 
Mar 27 
comment 
A “quadratic” triangular inequality
Thanks, Fedor ! 
Mar 27 
revised 
A “quadratic” triangular inequality
added 155 characters in body 
Mar 27 
revised 
A “quadratic” triangular inequality
added 435 characters in body 
Mar 27 
revised 
A “quadratic” triangular inequality
added 110 characters in body 
Mar 27 
asked  A “quadratic” triangular inequality 
Mar 20 
answered  BlowUp for SemiLinear Wave Equations 
Mar 12 
awarded  Popular Question 
Mar 10 
comment 
Density of smooth functions in Sobolev space, respecting nonnegative traces
Actually, a Theorem due to Stampacchia says that if $\phi$ is a Lipschit functin, then $u\mapsto\phi\circ u$ is a Lipschitz function from $W^{1,p}$ into itself. Apply this to $\phi(s)=s^+$. 
Mar 4 
comment 
Classification of PDE
@Qfwfq. Right, Schroedinger's equation is linear, but the number of independent variables is $1+3N$ where $N$ is the number of particles (electrons, protons, neutrons, ...) In practice, it is untractable by numerical schemes. For this reason, one makes approximations (density functional, HartreeFock, Slatter and so on), which replace it by a nonlinear equation in $1+3$ variables. 
Feb 23 
comment 
Reflection of light from function graph
Although I liked Bob's answer (and voted it), I doubt that it solves completely the question, because it deals with only one light ray. It proves that every light ray $R$ must bounce back at some abcissa $X(R)$. But it does not prove that $XR)$ is bounded independently on the initial direction of the ray. 
Feb 19 
comment 
Nonnegative decomposition of a nonnegative matrix
Thanks a lot ! I guessed that it should be documented. I didn't know the terminology. 
Feb 19 
accepted  Nonnegative decomposition of a nonnegative matrix 
Feb 19 
asked  Nonnegative decomposition of a nonnegative matrix 
Feb 18 
answered  On primitive type matrix ranks 
Feb 18 
answered  Boundary energy estimate of wave equations 
Feb 17 
revised 
A geometric property of singular matrices
added 450 characters in body 