Formation of Singularities for Weakly Non-Linear N×N Hyperbolic Systems

We present some results on the formation of singularities for C^1 - solutions of the quasi-linear N × N strictly hyperbolic system Ut + A(U )Ux = 0 in [0, +∞) × Rx . Under certain weak non-linearity conditions (weaker than genuine non-linearity), we prove that the first order derivative of the solution blows-up in finite time.

Sharp Bounds on the Number of Resonances for Symmertic Systems II. Non-Compactly Supported Perturbations

We extend the results in [5] to non-compactly supported perturbations for a class of symmetric first order systems.

Existence Theorems for Non-Cooperative Elliptic Systems

2010 Mathematics Subject Classification: 35J65, 35K60, 35B05, 35R05.