scholarly journals Invariant discretization of partial differential equations admitting infinite-dimensional symmetry groups

2015 ◽  
Vol 21 (4) ◽  
pp. 285-318 ◽  
Author(s):  
Raphaël Rebelo ◽  
Francis Valiquette
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Symmetry Groups ◽  
Partial Differential ◽  
Infinite Dimensional

scholarly journals Recent Advances in Symmetry Groups and Conservation Laws for Partial Differential Equations and Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-2 ◽  
Author(s):  
Maria Gandarias ◽  
Mariano Torrisi ◽  
Maria Bruzón ◽  
Rita Tracinà ◽  
Chaudry Masood Khalique
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Conservation Laws ◽  
Symmetry Groups ◽  
Partial Differential ◽  
Recent Advances

B-determining equations: applications to nonlinear partial differential equations

1995 ◽  
Vol 6 (3) ◽  
pp. 265-286 ◽  
Author(s):  
O. V. Kaptsov
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fluid Mechanics ◽  
Exact Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Symmetry Groups ◽  
Partial Differential ◽  
Physical Importance

We introduce the concept of B-determining equations of a system of partial differential equations that generalize the defining equations of the symmetry groups. We show how this concept may be applied to obtain exact solutions of partial differential equations. The exposition is reasonable self-contained, and supplemented by examples of direct physical importance, chosen from fluid mechanics.

scholarly journals Infinite-dimensional linear algebra and solvability of partial differential equations

2021 ◽  
Vol 13 ◽  
Author(s):  
Todor D. Todorov
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Linear Algebra ◽  
Differential Operators ◽  
Test Functions ◽  
Partial Differential ◽  
Infinite Dimensional ◽  
Partial Differential Operators ◽  
Linear Partial Differential Operators ◽  
Regular Operators

  We discuss linear algebra of infinite-dimensional vector spaces in terms of algebraic (Hamel) bases. As an application we prove the surjectivity of a large class of linear partial differential operators with smooth ($\mathcal C^\infty$-coefficients) coefficients, called in the article \emph{regular}, acting on the algebraic dual $\mathcal D^*(\Omega)$ of the space of test-functions $\mathcal D(\Omega)$. The surjectivity of the partial differential operators guarantees solvability of the corresponding partial differential equations within $\mathcal D^*(\Omega)$. We discuss our result in contrast to and comparison with similar results about the restrictions of the regular operators on the space of Schwartz distribution $\mathcal D^\prime(\Omega)$, where these operators are often non-surjective. 

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