In this paper we consider second order parabolic partial differential equations on the infinite strip. We confine our attention to the quasi-linear equations, and in particular, the problem
(0-1) u͙(t,x) = f(u)uxx(t.x) , (t,x) ε(0,T)x(-∞,∞) ≡ DT, T>0
u(0,x) = u0(x) , x ε (-∞,∞).
Existence, uniqueness and properties of the solution are discussed. These results can be immediately generalized to problems where the differential equation is of the form u͙(t,x) = f(t,x,u)u xx(t,x).
Level of Degree
Mathematics & Statistics
First Committee Member (Chair)
I. I. Kolodner
Second Committee Member
Morris S. Hendrickson
Third Committee Member
United States Army Research Office
Hermes, Henry. "On the Initial Value Problem For the Quasi-Linear Parabolic Partial Differential Equation." (1962). https://digitalrepository.unm.edu/math_etds/126