INVARIANT SUBSPACES IN UNBOUNDED DOMAINS
Проблемы анализа, 2021 We study subspaces of functions analytic in an unbounded convex domain of the complex plane and invariant with respect to the differentiation operator.
A. S. Krivosheev, O. A. Krivosheeva
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The unified transform for mixed boundary condition problems in unbounded domains. [PDF]
Proc Math Phys Eng Sci, 2019 This paper implements the unified transform to problems in unbounded domains with solutions having corner singularities. Consequently, a wide variety of mixed boundary condition problems can be solved without the need for the Wiener–Hopf technique.
Colbrook MJ, Ayton LJ, Fokas AS.
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Random attractors for stochastic plate equations with memory in unbounded domains
Open Mathematics, 2021 In this paper, we investigate the dynamics of stochastic plate equations with memory in unbounded domains. More specifically, we obtain the uniform time estimates for solutions of the problem.
Yao Xiao Bin
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The concentration-compactness principle for fractional order Sobolev spaces in unbounded domains and applications to the generalized fractional Brezis–Nirenberg problem [PDF]
Nonlinear Differential Equations and Applications, 2018 In this paper we extend the well-known concentration-compactness principle for the Fractional Laplacian operator in unbounded domains. As an application we show sufficient conditions for the existence of solutions to some critical equations involving the
Julian Fernández Bonder +2 more
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On a nonolinear wave equation in unbounded domains [PDF]
International Journal of Mathematics and Mathematical Sciences, 1988 We study existence and uniqeness of the nonlinear wave equation∂2u∂t2+M(x,∫|∇u(x,t)|2dx+∫|u(x,t)|2dx)(−Δu+u)=0in unbounded domains. The above model describes nonlinear wave phenomenon in non-homogeneous media.
Carlos Frederico Vasconcellos
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Modulation Equation and SPDEs on Unbounded Domains [PDF]
Communications in Mathematical Physics, 2017 We consider the approximation via modulation equations for nonlinear SPDEs on unbounded domains with additive space-time white noise. Close to a bifurcation an infinite band of eigenvalues changes stability, and we study the impact of small space–time ...
L. Bianchi, D. Blömker, G. Schneider
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Review and Recent Developments on the Perfectly Matched Layer (PML) Method for the Numerical Modeling and Simulation of Elastic Wave Propagation in Unbounded Domains [PDF]
Archives of Computational Methods in Engineering, 2021 This review article revisits and outlines the perfectly matched layer (PML) method and its various formulations developed over the past 25 years for the numerical modeling and simulation of wave propagation in unbounded media.
F. Pled, C. Desceliers
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Adaptive Hermite Spectral Methods in Unbounded Domains [PDF]
Applied Numerical Mathematics, 2022 Recently, new adaptive techniques were developed that greatly improved the efficiency of solving PDEs using spectral methods. These adaptive spectral techniques are especially suited for accurately solving problems in unbounded domains and require the ...
T. Chou, Sihong Shao, Mingtao Xia
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Solving a Dirichlet problem on unbounded domains via a conformal transformation [PDF]
Mathematische Annalen, 2022 In this paper, we solve the p-Dirichlet problem for Besov boundary data on unbounded uniform domains with bounded boundaries when the domain is equipped with a doubling measure satisfying a Poincaré inequality. This is accomplished by studying a class of
Ryan Gibara +2 more
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Fractional Calderón problems and Poincaré inequalities on unbounded domains [PDF]
Journal of Spectral Theory, 2022 We generalize many recent uniqueness results on the fractional Calder\'on problem to cover the cases of all domains with nonempty exterior. The highlight of our work is the characterization of uniqueness and nonuniqueness of partial data inverse problems
J. Railo, Philipp Zimmermann
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