DISSIPATION FUNCTIONS AND INVARIANT IMBEDDING, I

Abstract

In a series of papers dating from 1956, the authors have used the theory of invariant imbedding to derive a variety of nonlinear functional equations for the description of radiative transfer, neutron transport, diffusion and heat conduction, scattering and random walk, and wave propagation. In this paper a new method is presented for establishing the existence of solutions of these equations in the cases where no creation of matter is involved. This method is based upon the introduction of a new class of physically important functions, the dissipation functions. Combining these new functions with the functions utilized in the past, the reflection and transmission functions, we easily obtain a basic conservation relation upon which all else hinges. The uniqueness proofs follow conventional lines.

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Document Details

Document Type
Technical Report
Publication Date
Apr 22, 1960
Accession Number
AD0616588

Entities

People

  • G. M. Wing
  • Richard E. Bellman
  • Robert E. Kalaba

Organizations

  • RAND Corporation

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Corporations
  • Differential Equations
  • Dissipation
  • Equations
  • Mathematical Models
  • Mathematics
  • Models
  • New York
  • Nonlinear Differential Equations
  • Particles
  • Radiative Transfer
  • Random Walk
  • Scattering
  • Time Dependence
  • Transmission Lines
  • Transport Ships
  • Wave Propagation

Readers

  • Control Systems Engineering.
  • Statistical inference.
  • Theoretical Analysis.