Michael Eydenberg, Maria Cristina Mariani
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
to give existence of solutions
for certain classes of distributions
.
We also study growth conditions for smooth solutions of certain
parabolic equations on
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.
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Michael Eydenberg Department of Mathematical Sciences New Mexico State University Las Cruces, NM 88003-8001, USA email: mseyden@nmsu.edu | |
María Cristina Mariani Department of Mathematical Sciences University of Texas, El Paso, Bell Hall 124 El Paso, Texas 79968-0514, USA email: mcmariani@utep.edu |
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