Remarks on blow up time for solutions of a nonlinear diffusion system with time dependent coefficients

2000 Mathematics Subject Classification: 35K55, 35K60.

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.

Critical Exponents of Semilinear Equations via the Feynman-Kac Formula

2000 Mathematics Subject Classification: 60H30, 35K55, 35K57, 35B35.

Dunkl-Schrödinger Equations with and without Quadratic Potentials

2000 Mathematics Subject Classification: Primary 42A38. Secondary 42B10.