What comes on top of a generator of a PDE?

  • Context: Graduate 
  • Thread starter Thread starter Omega0
  • Start date Start date
  • Tags Tags
    Generator Pde
Click For Summary
SUMMARY

The discussion centers on the concept of generators in the context of Partial Differential Equations (PDEs) and the calculus of variations. It questions the existence of higher-level mathematical constructs that serve as generators for the generators of PDEs. The heat equation is specifically noted as an example that does not originate from a variational principle, highlighting the complexity and depth of mathematical frameworks in physics.

PREREQUISITES
  • Understanding of Partial Differential Equations (PDEs)
  • Familiarity with calculus of variations
  • Knowledge of mathematical principles in physics
  • Basic concepts of variational principles
NEXT STEPS
  • Research advanced topics in the calculus of variations
  • Explore the theory of generators in mathematical physics
  • Study the derivation and implications of the heat equation
  • Investigate higher-order mathematical frameworks in PDE theory
USEFUL FOR

Mathematicians, physicists, and advanced students interested in the theoretical foundations of PDEs and the calculus of variations.

Omega0
Messages
215
Reaction score
52
From some principles in nature we are using in physics the calculus of variations. Let me call it a generator for PDE's. My question: Are there levels above? What I mean is: Is there mathematics where you have principles where the solutions are generators for the generators for PDEs ?
What about generators for the generators for the generators?
 
Physics news on Phys.org
Omega0 said:
From some principles in nature we are using in physics the calculus of variations. Let me call it a generator for PDE's.
The heat equation for example does not come from a variational principle
 

Similar threads

Undergrad Adding total time derivative to Lagrangian/Canonical Transformations
  • · Replies 2 ·
Replies
2
Views
673
Undergrad Why is the negative sign in the equation for motional EMF often discarded?
  • · Replies 7 ·
Replies
7
Views
4K
Copper Losses in an Electric Generator
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Ever-increasing amplitude of the induced impulse?
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Bernoulli, lift and cause & effect
  • · Replies 30 ·
2
Replies
30
Views
4K
Applied Bibliography on integration and ODE/PDE solving techniques for physics
  • · Replies 12 ·
Replies
12
Views
2K
Undergrad What Generates Sound Waves and How Do They Travel Through Different Mediums?
  • · Replies 31 ·
2
Replies
31
Views
4K
AC generator, current and ground
  • · Replies 26 ·
Replies
26
Views
3K
Graduate SL(3,R) Generators and their Interpretation
  • · Replies 5 ·
Replies
5
Views
4K
ABC reference frame synchronous generator modelling in Ltspice
  • · Replies 1 ·
Replies
1
Views
3K