#### Publication Date

5-22-1962

#### Abstract

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)u_{xx}(t.x) , (t,x) ε(0,T)x(-∞,∞) ≡ D_{T, T>0}

u(0,x) = u_{0}(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).

#### Degree Name

Mathematics

#### Level of Degree

Doctoral

#### Department Name

Mathematics & Statistics

#### First Committee Member (Chair)

I. I. Kolodner

#### Second Committee Member

Morris S. Hendrickson

#### Third Committee Member

Oswald Wyler

#### Project Sponsors

United States Army Research Office

#### Language

English

#### Document Type

Dissertation

#### Recommended Citation

Hermes, Henry. "On the Initial Value Problem For the Quasi-Linear Parabolic Partial Differential Equation." (1962). https://digitalrepository.unm.edu/math_etds/126