Blow-up solutions in semilinear heat equations refer to phenomena where solutions become unbounded in finite time, an occurrence that has far‐reaching implications for the study of nonlinear partial ...

When we think about heat traveling through a material, we typically picture diffusive transport, a process that transfers heat from high-temperature to low-temperature as particles and molecules bump ...

We examine a heat problem in 1D. Assume that a rod with given temperature distribution u_0(x) is cooled to temperature 0 on the exteriors at 0 and pi. Assume that u(x,t) for the Temperature at point x ...