Stability analysis for semilinear parabolic problems in general unbounded domains

Elliptic and parabolic problems in unbounded domains

We consider elliptic and parabolic problems in unbounded domains. We give general existence and regularity results in Besov spaces and semi-explicit representation formulas via operatorvalued fundamental solutions which turn out to be a powerful tool to derive a series of qualitative results about the solutions. We give a sample of possible applications including asymptotic behavior in the larg...

Computational Solution of Blow-Up Problems for Semilinear Parabolic PDEs on Unbounded Domains

A numerical treatement of a model of semilinear parabolic equations on unbounded domain where the solutions blow up in finite time is presented. The numerical approximation requires selecting an appropriate bounded computational domain. The authors present suitable local absorbing boundary conditions (LABCs) in order to derive the bounded computational domain. A unified approach to derive such ...

Semilinear parabolic problems

Numerical Analysis of Semilinear Parabolic Problems

In these lectures I discuss error analysis techniques for nite element methods for systems of reaction-diiusion equations with applications in dynamical systems theory. The emphasis is on pedagogical aspects and analysis techniques rather than on results. The list of techniques discussed include: analytic semigroup, parabolic smoothing, non-smooth data error estimate, a priori error estimate, a...

Numerical Blow-up of Semilinear Parabolic PDEs on Unbounded Domains in ℝ2

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 ...