Galois theory for the family of partial differential equations? ? ?=0

1970 ◽  
Vol 114 (1) ◽  
pp. 22-32
Author(s):  
Abul Maksud Sayied
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Galois Theory ◽  
Partial Differential ◽  
The Family

Ground States and Singular Ground States for Quasilinear Partial Differential Equations with Critical Exponent in the Perturbative Case

2004 ◽  
Vol 4 (1) ◽  
Author(s):  
Matteo Franca ◽  
Russell Johnson
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exponential Dichotomy ◽  
Invariant Manifolds ◽  
Ground States ◽  
Elliptic Partial Differential Equations ◽  
Partial Differential ◽  
Quasilinear Partial Differential Equations ◽  
Melnikov Functions ◽  
The Family

AbstractWe study the structure of the family of radially symmetric ground states and singular ground states for certain elliptic partial differential equations with p- Laplacian. We use methods of Dynamical systems such as Melnikov functions, invariant manifolds, and exponential dichotomy.

scholarly journals Stochastic partial differential equations driven by space-time fractional noises

2019 ◽  
Vol 19 (02) ◽  
pp. 1950012
Author(s):  
Ying Hu ◽  
Yiming Jiang ◽  
Zhongmin Qian
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Space Time ◽  
Partial Differential ◽  
The Family ◽  
Non Local ◽  
Fractional Noises

In this paper, we study a class of stochastic partial differential equations (SPDEs) driven by space-time fractional noises. Our method consists in studying at first the non-local SPDEs and thereafter showing the convergence of the family of these equations. The limit gives the solution of the SPDE.

scholarly journals Symmetry Analysis, Exact Solutions and Conservation Laws of a Benjamin–Bona–Mahony–Burgers Equation in 2+1-Dimensions

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2083
Author(s):  
María S. Bruzón ◽  
Tamara M. Garrido-Letrán ◽  
Rafael de la Rosa
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Soliton Solutions ◽  
Third Order ◽  
Partial Differential ◽  
Symmetry Reductions ◽  
Multipliers Method ◽  
The Family

The Benjamin–Bona–Mahony equation describes the unidirectional propagation of small-amplitude long waves on the surface of water in a channel. In this paper, we consider a family of generalized Benjamin–Bona–Mahony–Burgers equations depending on three arbitrary constants and an arbitrary function G(u). We study this family from the standpoint of the theory of symmetry reductions of partial differential equations. Firstly, we obtain the Lie point symmetries admitted by the considered family. Moreover, taking into account the admitted point symmetries, we perform symmetry reductions. In particular, for G′(u)≠0, we construct an optimal system of one-dimensional subalgebras for each maximal Lie algebra and deduce the corresponding (1+1)-dimensional nonlinear third-order partial differential equations. Then, we apply Kudryashov’s method to look for exact solutions of the nonlinear differential equation. We also determine line soliton solutions of the family of equations in a particular case. Lastly, through the multipliers method, we have constructed low-order conservation laws admitted by the family of equations.

Partial Differential Equations

2020 ◽  
Author(s):  
A. K. Nandakumaran ◽  
P. S. Datti
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential
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