Towards the Differences in Behaviour of Solutions of Linear and Non-linear Heat-conduction Equations
Authors
Liudmila Ilinichna Rubina
Institute of Mathematics and Mechanics of the Russian Academy of Sciences (Ural branch)
Oleg Nikolaevich Ul?yanov
Institute of Mathematics and Mechanics of the Russian Academy of Sciences (Ural branch)
Keywords:
non-linear equations in partial derivatives, heat-conduction equations, exact solutions, surfaces of the level
Abstract
The linear and non-linear heat-conduction equations are analyzed by the previously initiated geometrical method of analyzing linear and non-linear equations in partial derivatives. The reason of the difference in behavior of solutions of equations under consideration was stated, as well as the reason of aggravation of the non-linear equation. A class of solutions of linear equations that represents the surfaces of the levels of non-linear heat-conduction equations was excluded.
Author Biographies
Liudmila Ilinichna Rubina, Institute of Mathematics and Mechanics of the Russian Academy of Sciences (Ural branch)
Cand. Sc. (Physics and Mathematics), Senior Staff Scientist
Oleg Nikolaevich Ul?yanov, Institute of Mathematics and Mechanics of the Russian Academy of Sciences (Ural branch)
