Results 81 to 90 of about 188 (177)

APPLICATION OF BACKLUND DIFFERENTIAL CONSTRAINT FOR CONSTRUCTING EXACT SOLUTIONS OF NONLINEAR HYPERBOLIC EQUATIONS

Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2020
Background. Finding exact solutions of nonlinear partial differential equations is one of the main problems of the nonlinear systems theory. A number of methods have been developed for integrable systems, but due to the complexity of various nonlinear
T. V. Red'kina, O. V. Novikova
doaj   +1 more source

BACKLUND TRANSFORMATIONS FOR LIOUVILLE’S EQUATIONS WITH EXPONENTIAL NONLINEARITY

Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2020
Background. The study of Backlund 's transformations is one of the current topics in the theory of differential equations in partial derivatives. Such transformations are used to find solutions to nonlinear differential equations, including solitonic ...
T. V. Red'kina, O. V. Novikova
doaj   +1 more source

On Monge-Ampere equations with homogeneous right hand side

, 2007
We study the regularity and behavior at the origin of solutions to the two-dimensional degenerate Monge-Ampere equation with homogeneous right hand side of degree alpha, alpha>-2. We show that when alpha > 0, solutions admit only two possible behaviors near the origin, radial and non-radial. We also show that the radial behavior is unstable.
Daskalopoulos, Pangiota, Savin, Ovidiu
openaire   +2 more sources

Qualitative properties of solutions for dual fractional parabolic equations involving nonlocal Monge-Ampère operator

Advances in Nonlinear Analysis
In this article, we mainly study the qualitative properties of solutions for dual fractional-order parabolic equations with nonlocal Monge-Ampère operators in different domains ∂tβμ(y,t)−Dατμ(y,t)=f(μ(y,t)).{\partial }_{t}^{\beta }\mu \left(y,t)-{D}_ ...
Yang Zerong, He Yong
doaj   +1 more source

Design of freeform mirrors using the concentric rings method. [PDF]

Heliyon, 2023
González-García J, Santiago-Alvarado A, Cruz-Félix AS.   +2 more
europepmc   +1 more source

Monotonicity of solutions for parabolic equations involving nonlocal Monge-Ampère operator

Advances in Nonlinear Analysis
In this article, we consider the parabolic equations with nonlocal Monge-Ampère operators ∂u∂t(x,t)−Dsθu(x,t)=f(u(x,t)),(x,t)∈R+n×R.\frac{\partial u}{\partial t}\left(x,t)-{D}_{s}^{\theta }u\left(x,t)=f\left(u\left(x,t)),\hspace{1.0em}\left(x,t)\in ...
Du Guangwei, Wang Xinjing
doaj   +1 more source

Averaging Effects and Their Applications to Fractional Elliptic and Parabolic Equations

Fractal and Fractional
The averaging effect is a distinctive property possessed by fractional operators. In recent years, it has emerged as a powerful tool in the study of qualitative properties of solutions to fractional elliptic and parabolic equations.
Wenxiong Chen, Yahong Guo
doaj   +1 more source

Optimal transport and control of active drops. [PDF]

Proc Natl Acad Sci U S A, 2022
Shankar S, Raju V, Mahadevan L.
europepmc   +1 more source

The Monge-Ampere equation: various forms and numerical methods

, 2009
24 pages, 2 tables, 5 figures, 32 references. Submitted to J. Computational Physics. Times of runs added, multiple improvements of the manuscript implemented.
Zheligovsky, V., Podvigina, O., Frisch, U.   +2 more
openaire   +2 more sources

Recursions of Symmetry Orbits and Reduction without Reduction

Symmetry, Integrability and Geometry: Methods and Applications, 2011
We consider a four-dimensional PDE possessing partner symmetries mainly on the example of complex Monge-Ampère equation (CMA). We use simultaneously two pairs of symmetries related by a recursion relation, which are mutually complex conjugate for CMA ...
Andrei A. Malykh, Mikhail B. Sheftel
doaj   +1 more source