Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 91, pp. 1-17.
Title: Distribution-valued weak solutions to a parabolic
problem arising in financial mathematics
Authors: Michael Eydenberg (New Mexico State Univ., Las Cruces, NM, USA)
Maria Cristina Mariani (Univ. of Texas, El Paso, TX, USA)
Abstract:
We study distribution-valued solutions to a parabolic problem that
arises from a model of the Black-Scholes equation in option pricing.
We give a minor generalization of known existence and uniqueness
results for solutions in bounded domains
$\Omega \subset \mathbb{R}^{n+1}$ to give existence of solutions
for certain classes of distributions $f\in \mathcal{D}'(\Omega)$.
We also study growth conditions for smooth solutions of certain
parabolic equations on $\mathbb{R}^n\times (0,T)$ that have
initial values in the space of distributions.
Submitted September 10, 2008. Published July 30, 2009.
Math Subject Classifications: 35K10, 35D30, 91B28.
Key Words: Weak solutions; parabolic differential equations;
Black-Scholes type equations.