On the Initial Value Problem For the Quasi-Linear Parabolic Partial Differential Equation

Author

Henry Hermes

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) = 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).

Degree Name

Mathematics

Level of Degree

Doctoral

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Ignace 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