Contributions to Books:

S. Stanek, G. Pulverer, E. Weinmüller:
"Analysis and numerical simulation of positive and dead core solutions of singular two-point boundary value problems";
in: "ASC Report 18/2007", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2007, ISBN: 978-3-902627-00-1.

English abstract:
We investigate the solvability of the Dirichlet boundary value problem
u′′(t) = g(u(t)), ≥ 0, u(0) = 1, u(1) = 1,
where is a nonnegative parameter. We discuss the existence of multiple positive
solutions and show that for certain values of , there also exist solutions that
vanish on a subinterval [ , 1 − ] ⊂ (0, 1), the so-called dead core solutions. In
order to illustrate the theoretical findings, we present computational results for
g(u) = 1/√u, computed using the collocation method implemented in bvpsuite,
a new version of the standard MATLAB code sbvp1.0.

Singular Dirichlet boundary value problem, positive solution, dead

Electronic version of the publication:

Created from the Publication Database of the Vienna University of Technology.