The equation u t =Δu+u p with homogeneous Dirichlet boundary conditions has solutions with blow-up if p>1. An adaptive time-step procedure is given to reproduce the asymptotic behavior of the solutions in the numerical ...

© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.Although macrophages are part of the human immune system, it has been remarkably observed in laboratory experiments that decreasing its number can slow down the ...

We construct a periodic solution to the semilinear heat equation with power nonlinearity, in one space dimension, which blows up in finite time T only at one blow-up point. We also give a sharp description of its blow-up ...

In this paper we deal with positive radially symmetric solutions for a boundary value problem containing a strongly nonlinear operator. The proof of existence of positive solutions that we give uses the blow-up method as ...

Understanding how tangential singularities evolve under smoothing processes was one of the first problem concerning regularization of Filippov systems. In this paper, we are interested in C n -regularizations of Filippov ...

In this paper, we investigate the existence, uniqueness, exponential decay, and blow-up behavior of the viscoelastic beam equation involving the (Formula presented.) -Laplacian operator, strong damping, and a logarithmic ...