Abstract In this paper, we consider the sign of solutions to Cauchy problems linear and semilinear polyharmonic heat equations. for higher order parabolic equations have no positivity preserving property in general, however, it is expected that these are eventually globally positive if initial data decay slowly enough. We first show existence threshold rate datum which separates whether corresp...

Abstract Explicit stabilized integrators are an efficient alternative to implicit or semiimplicit methods avoid the severe time-step restriction faced by standard explicit applied stiff diffusion problems. In this paper we provide a fully discrete strong convergence analysis of family coupled with finite element for class parabolic semilinear deterministic and stochastic partial differential eq...

We study integrability conditions for existence and nonexistence of a local-in-time integral solution fractional semilinear heat equations with rather general growing nonlinearities in uniformly local $$L^p$$ spaces. Our main results about this matter consist Theorems 1.4, 1.6, 5.1 5.3. introduce supersolution an equation which can be applied to nonlocal parabolic equation. When the nonlinear t...

We establish optimal order a priori error estimates for implicit– explicit BDF methods for abstract semilinear parabolic equations with timedependent operators in a complex Banach space setting, under a sharp condition on the non-self-adjointness of the linear operator. Our approach relies on the discrete maximal parabolic regularity of implicit BDF schemes for autonomous linear parabolic equat...

We study the numerical solution of semilinear parabolic PDEs on unbounded spatial domains in R2 whose solutions blow up in finite time. Of particular interest are the cases where = R2 or is a sectorial domain in R2. We derive the nonlinear absorbing boundary conditions for corresponding, suitably chosen computational domains and then employ a simple adaptive time-stepping scheme to compute the ...