Joel Smoller

Large Time Behavior of Solutions of Systems of Nonlinear Reaction-Diffusion Equations

We discuss the asymptotic behavior of solutions of weakly coupled parabolic equations describing systems undergoing diffusion, convection and nonlinear interaction in a bounded spatial domain,

Global Bifurcation of Steady-State Solutions

\Omega

Global solutions of the relativistic Euler equations

. If the system admits a bounded invariant region

On the vacuum state for the isentropic gas dynamics equations

\Sigma

Smooth static solutions of the Einstein/Yang-Mills equations

of phase space then we isolate a parameter

Global solutions for an extended class of hyperbolic systems of conservation laws

\sigma

Existence of infinitely many smooth, static, global solutions of the Einstein/Yang-Mills equations

which depends upon the size of

Global analysis of a system of predator-prey equations

\Omega

Solutions in the large for certain nonlinear parabolic systems

, the lower bound for the diffusion matrix, the magnitude of convection and a measure of the strength or sensitivity of the reaction. For

Existence of black hole solutions for the Einstein-Yang/Mills equations

\sigma > 0