Advances in Nonlinear AnalysisIn this article, we study the following Choquard equation: −Δu+u=(Iα⋆u2)u,x∈R3,-\Delta u+u=\left({{\rm{I}}}_{\alpha }\star {u}^{2})u,\hspace{1.0em}x\in {{\mathbb{R}}}^{3}, where Iα{{\rm{I}}}_{\alpha } is the Riesz potential and α\alpha is sufficiently ...
Luo Huxiao, Zhang Dingliang, Xu Yating
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Rapid exponential stabilization of a 1-D transmission wave equation with in-domain anti-damping [PDF]
Vol. 19, No. 6, pp. 1-11, November 2017, 2018 We consider the problem of pointwise stabilization of a one-dimensional wave equation with an internal spatially varying anti-damping term. We design a feedback law based on the backstepping method and prove exponential stability of the closed-loop system with a desired decay rate.
arxiv +1 more source
Diffuse-interface approximation and weak–strong uniqueness of anisotropic mean curvature flow
European Journal of Applied MathematicsThe purpose of this paper is to derive anisotropic mean curvature flow as the limit of the anisotropic Allen–Cahn equation. We rely on distributional solution concepts for both the diffuse and sharp interface models and prove convergence using relative ...
Tim Laux +2 more
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Conditional stability for backward parabolic operators with Osgood continuous coefficients [PDF]
Annali di Matematica (2019), 2019 We prove continuous dependence on initial data for a backward parabolic operator whose leading coefficients are Osgodd continuous in time. This result fills the gap between uniqueness and continuity results obtained so far.
arxiv +1 more source
Contracting T^2 symmetry local existence for Einstein-Vlasov-Scalar field system [PDF]
arXiv, 2021 The evolution of self-gravitating collision-less matter and scalar waves within the general relativity context is described by Einstein and Vlasov equations. The sources of Einstein equations are generated by a distribution function and a scalar field, respectively subject to the Vlasov and wave equations.
arxiv
European Journal of Applied MathematicsThis article studies the dynamical behaviour of classical solutions of a hyperbolic system of balance laws, derived from a chemotaxis model with logarithmic sensitivity, with time-dependent boundary conditions. It is shown that under suitable assumptions
Padi Fuster Aguilera, Kun Zhao
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Well-posedness for the Cauchy problem for a fractional porous medium equation with variable density in one space dimension [PDF]
arXiv, 2012 We study existence and uniqueness of bounded solutions to a fractional nonlinear porous medium equation with a variable density, in one space dimension.
arxiv
Long time decay of incompressible convective Brinkman-Forchheimer in L2(ℝ3)
Demonstratio MathematicaIn this article, we study the global existence, uniqueness, and continuity for the solution of incompressible convective Brinkman-Forchheimer on the whole space R3{{\mathbb{R}}}^{3} when 4μβ≥14\mu \beta \ge 1.
Jlali Lotfi, Benameur Jamel
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Uniqueness and Nondegeneracy of Ground States for Choquard Equations in three dimensions [PDF]
arXiv, 2015 We obtain uniqueness and nondegeneracy results for ground states of Choquard equations $-\Delta u+u=\left(|x|^{-1}\ast|u|^{p}\right)|u|^{p-2}u$ in $\mathbb{R}^{3}$, provided that $p>2$ and $p$ is sufficiently close to 2.
arxiv
Planar Immersions with Prescribed Curl and Jacobian Determinant are Unique [PDF]
arXiv, 2021 We prove that immersions of planar domains are uniquely specified by their Jacobian determinant, curl function, and boundary values. This settles the two-dimensional version of an outstanding conjecture related to a particular grid generation method in computer graphics.
arxiv