AbstractUnstable growth phenomena in spatially discrete wave equations are
studied. We characterize sets of initial states leading to instability and collapse and
obtain analytical predictions for the blow-up time. The theoretical predictions are con-
trasted with the numerical solutions computed by a variety of schemes. The behavior
of the systems in the continuum limit and the impact of discreteness and friction are
discussed.
Abstract
In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution
u
(
x
,
t
)
u(x,t)
blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.
Five types of blow-up in a semilinear fourth-order reaction–diffusion equation: an analytic–numerical approach