Is this pde analytically solvable?

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Discussion Overview

The discussion revolves around the possibility of deriving an analytical solution to a partial differential equation (PDE) related to a spatial model for animal movement. Participants explore the conditions under which such a solution might exist, particularly focusing on the function theta, which is dependent on variables x and t.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant, a theoretical biologist, seeks guidance on whether an analytical solution for y(x,t) can be derived from their PDE structure.
  • Another participant notes that the ability to derive an analytical solution depends on the specific form of the function theta(x,t) and questions what that function is.
  • There is a request for an attachment that presumably contains the equation, indicating that the discussion may hinge on visualizing the mathematical structure.

Areas of Agreement / Disagreement

Participants have not reached a consensus. The discussion includes uncertainty about the function theta(x,t) and its implications for finding an analytical solution.

Contextual Notes

The discussion lacks clarity on the specific form of the function theta(x,t), which is crucial for determining the solvability of the PDE. There are also missing details regarding the mathematical steps involved in the proposed solution.

nigels
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I'm a theoretical biologist in the process of developing a spatial model for animal movement. So far, I've arrived at the following structure of an equation (see attachment):
*theta is just some function of x and t.

Having never formally studied pde, I'm wondering whether one can, from this, derive an analytical solution to y(x,t) and, if so, how (or, what sources can I go to to find the solution)?
 
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I don't see an attachment...
 
hope it works this time

https://www.physicsforums.com/attachment.php?attachmentid=34793&d=1303613043
 
Last edited by a moderator:
I'm wondering whether one can, from this, derive an analytical solution to y(x,t)
Analytical solution can or cannot be derived, depending the form of the function theta(x,t)
What is the function theta(x,t) ?
 

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