This paper explores the application of blow-up criterion to Lorenz system establish possibility a finite-time outburst when quadratic term is present. The system, set differential equations that models atmospheric convection, known for its chaotic behavior and has been subject extensive research because sensitivity initial conditions. By analyzing using criterion, conditions under which can lea...

We discuss a new approach for the numerical computation of self-similar blow-up solutions of certain nonlinear partial differential equations. These solutions become unbounded in finite time at a single point at which there is a growing and increasingly narrow peak. Our main focus is on a quasilinear parabolic problem in one space dimension, but our approach can also be applied to other problem...