19,025 reputation
350130
bio website umpa.ens-lyon.fr/~serre
location Lyon, FRANCE
age 60
visits member for 4 years, 7 months
seen 3 hours ago

My research activity is mainly in PDEs, with applications to Physics, especially in Fluid Dynamics. I have written a 2-volume book on Conservation laws, and a book about the Hyperbolic IBVP (in collaboration with S. Benzoni-Gavage). I have edited in collaboration with S. Friedlander, a 4-volume 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 Blow-Up for Semi-Linear 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, Hartree-Fock, Slatter and so on), which replace it by a non-linear 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 Non-negative decomposition of a non-negative matrix
Thanks a lot ! I guessed that it should be documented. I didn't know the terminology.
Feb
19
accepted Non-negative decomposition of a non-negative matrix
Feb
19
asked Non-negative decomposition of a non-negative 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