Mathematics – Analysis of PDEs
Scientific paper
2010-05-12
Netw. Het. Media 2 (2007), 55-79
Mathematics
Analysis of PDEs
In comparison with the already published version of this paper (Netw. Het. Media 2 (2007), 55-79), a small gap in the proof of
Scientific paper
We consider a diffusion problem on a network on whose nodes we impose Dirichlet and generalized, non-local Kirchhoff-type conditions. We prove well-posedness of the associated initial value problem, and we exploit the theory of sub-Markovian and ultracontractive semigroups in order to obtain upper Gaussian estimates for the integral kernel. We conclude that the same diffusion problem is governed by an analytic semigroup acting on all $L^p$-type spaces as well as on suitable spaces of continuous functions. Stability and spectral issues are also discussed. As an application we discuss a system of semilinear equations on a network related to potential transmission problems arising in neurobiology.
No associations
LandOfFree
Gaussian estimates for a heat equation on a network does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Gaussian estimates for a heat equation on a network, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Gaussian estimates for a heat equation on a network will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-499397