AN EXPLICIT FORMULA FOR AN UNKNOWN COEFFICIENT IN A PARABOLIC DIFFERENTIAL EQUATION

Abstract

Let the heat equation, (du/dt) equals a(t)(d(du/dx)), be satisfied in a semi-infinite medium (x positive), where both a(t) and u(x,t) are unknown. If u(x,o) equals o, u(o,t) equals f(t) (where f is constant), and -a(t) (du/dt)(o,t) equals g(t), then under certain conditions on g(t), there is exactly one pair a(t), u(x,t) satisfying the differential equation and the boundary and initial conditions. Also, an explicit formula gives a(t) in terms of g(v), for v less than or equal to t.

Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1961
Accession Number
AD0264428

Entities

People

  • B. Frank Jr. Jones

Organizations

  • Rice University

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Coefficients
  • Differential Equations
  • Equations
  • Mathematics
  • Partial Differential Equations

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Linear Algebra