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Advances in Nonlinear Analysis, 2021 We study the wave inequality with a Hardy ...
Jleli Mohamed +2 more
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Parabolic Hessian Quotient Equation in Exterior Domain
MathematicsThis study mainly focuses on the parabolic Hessian quotient equation in the exterior domain. The existence and uniqueness of generalized parabolically symmetric solutions with generalized asymptotic behavior are proven using Perron’s method.
Huawei Zhao, Limei Dai
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A Perturbed Cauchy Viscoelastic Problem in an Exterior Domain
Mathematics, 2023 A Cauchy viscoelastic problem perturbed by an inverse-square potential, and posed in an exterior domain of RN, is considered under a Dirichlet boundary condition.
Bessem Samet, Calogero Vetro
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Hessian equations on exterior domain
Journal of Mathematical Analysis and Applications, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xu Cao, Ji-Guang Bao
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Energy decay rates for solutions of the wave equation with linear damping in exterior domain
Evolution Equations and Control Theory, 2016 In this paper we study the behavior of the energy and the $L^{2}$ norm of solutions of the wave equation with localized linear damping in exterior domain. Let $u$ be a solution of the wave system with initial data $\left( u_{0},u_{1}\right) $.
Moez Daoulatli
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Multiplicity results for classes of singular problems on an exterior domain
Discrete and Continuous Dynamical Systems, 2013 We study radial positive solutions to the singular boundary value problem \begin{equation*} \begin{cases} -\Delta_p u = \lambda K(|x|)\frac{f(u)}{u^\beta} \quad \mbox{in}~ \Omega,\\ ~~~u(x) = 0 \qquad \qquad \qquad \qquad~~\mbox{if}~|x|=r_0 ...
R Shivaji
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Maximal Hypersurfaces over Exterior Domains [PDF]
Communications on Pure and Applied Mathematics, 2020 Exterior problems for the maximal surface equation are studied. We obtain the precise asymptotic behavior of the exterior solution at infinity. We also prove that the exterior Dirichlet problem is uniquely solvable for admissible boundary data and prescribed asymptotic behavior at infinity. © 2020 Wiley Periodicals LLC.
Hong, Guanghao, Yuan, Yu
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Hardy’s inequality on exterior domains [PDF]
Proceedings of the American Mathematical Society, 2005 Let \(\Omega\) be an unbounded domain of \(\mathbb R^N\) with a compact boundary of class \(C^2\) and let \(p>1\) be a real number. Denote \(\delta\,(x)= \text{dist}\,(x,\partial\Omega)\) and set \[ \mu_p(\Omega)=\inf\left\{\int_\Omega | \nabla u|^p;\;u\in {\mathcal D}_0^{1,p}(\Omega),\;\int_\Omega | u/\delta |^pdx=1\right\} \] and \(c_{p,N}=\min\left\{
Chabrowski, J., Willem, M.
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NOTE ON THE PROBLEM OF MOTION OF VISCOUS FLUID AROUND A ROTATING AND TRANSLATING RIGID BODY
Acta Polytechnica, 2021 We consider the linearized and nonlinear systems describing the motion of incompressible flow around a rotating and translating rigid body Ɗ in the exterior domain Ω = ℝ3 \ Ɗ, where Ɗ ⊂ ℝ3 is open and bounded, with Lipschitz boundary.
Paul Deuring +2 more
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Blow‐up of solutions to semilinear strongly damped wave equations with different nonlinear terms in an exterior domain [PDF]
Mathematical methods in the applied sciences, 2019 In this paper, we consider the initial boundary value problem in an exterior domain for semilinear strongly damped wave equations with power nonlinear term of the derivative‐type |ut|q or the mixed‐type |u|p + |ut|q, where p, q > 1.
Wen-Hui Chen, A. Fino
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