Learning unbounded-domain spatiotemporal differential equations using adaptive spectral methods
Sign Up to like & getrecommendations! Published in 2024 at "Journal of Applied Mathematics and Computing"
DOI: 10.1007/s12190-024-02131-2
Abstract: Rapidly developing machine learning methods have stimulated research interest in computationally reconstructing differential equations (DEs) from observational data, providing insight into the underlying mechanistic models. In this paper, we propose a new neural-ODE-based method that… read more here.
Keywords: differential equations; unbounded domain; spectral methods; domain spatiotemporal ... See more keywords
On Some $\protect \overrightarrow {p(x)}$ Anisotropic Elliptic Equations in Unbounded Domain
Sign Up to like & getrecommendations! Published in 2021 at "Acta Mathematica Vietnamica"
DOI: 10.1007/s40306-021-00434-1
Abstract: We study a class of nonlinear elliptic problems with Dirichlet conditions in the framework of the Sobolev anisotropic spaces with variable exponent, involving an anisotropic operator on an unbounded domain ${\varOmega }\subset \mathbb {R}^{N} (N… read more here.
Keywords: unbounded domain; protect overrightarrow; anisotropic; overrightarrow anisotropic ... See more keywords
Existence of solutions for a fractional equation in an unbounded domain
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Mathematical Physics"
DOI: 10.1063/1.5121762
Abstract: This paper focuses on the scalar field equation Dx2αu−νu−uyy=f(u), where α ∈ (0, 1), (x,y)∈RN×(−L,L)⊂RN+1, with N ≥ 1 and Dx2α stands for the fractional Laplacian. By using several variational methods, we establish the existence,… read more here.
Keywords: unbounded domain; solutions fractional; existence solutions; fractional equation ... See more keywords
The entropy solution of a reaction–diffusion equation on an unbounded domain
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Inequalities and Applications"
DOI: 10.1186/s13660-019-1956-3
Abstract: The degenerate parabolic equations from the reaction–diffusion problems are considered on an unbounded domain Ω⊂RN$\varOmega\subset\mathbb {R}^{N}$. It is expected that only a partial boundary should be imposed the homogeneous boundary value, but how to give… read more here.
Keywords: partial boundary; reaction diffusion; unbounded domain;
Regularized Solution of the Cauchy Problem in an Unbounded Domain
Sign Up to like & getrecommendations! Published in 2022 at "Symmetry"
DOI: 10.3390/sym14081682
Abstract: In this paper, using the construction of the Carleman matrix, we explicitly find a regularized solution of the Cauchy problem for matrix factorizations of the Helmholtz equation in a three-dimensional unbounded domain. read more here.
Keywords: solution cauchy; unbounded domain; cauchy problem; regularized solution ... See more keywords
Existence Result for Fractional Differential Equation on Unbounded Domain
Sign Up to like & getrecommendations! Published in 2024 at "Kragujevac Journal of Mathematics"
DOI: 10.46793/kgjmat2405.755b
Abstract: In this article, we establish certain sufficient conditions to show the existence of solutions of boundary value problem for fractional differential equations on the half-line in a Fréchet space. The main result is based on… read more here.
Keywords: fractional differential; differential equation; unbounded domain; equation unbounded ... See more keywords