Mamoru Okamoto. Source: Advances in Differential Equations, Volume 23, Number 9/10, 751--792.Abstract: We consider the long-time behavior of solutions to the fifth-order modified KdV-type equation. For the local-in-time well-posedness, we show that regularity conditions where by a tri-linear...
Isao Kato, Shinya Kinoshita. Source: Advances in Differential Equations, Volume 23, Number 9/10, 725--750.Abstract: We study the Cauchy problem of the Klein-Gordon-Zakharov system in spatial dimension $d \ge 5$ with initial datum $(u, \partial_t u, n, \partial_t n)|_{t=0} \in H^{s+1}(\mathbb{R}^d)...
Masashi Misawa, Nobumitsu Nakauchi. Source: Advances in Differential Equations, Volume 23, Number 9/10, 693--724.Abstract: In our previous papers, we introduce symphonic maps ([9]) and show a Hölder continuity of symphonic maps from domains of $\mathbb{R}^4$ into the spheres ([6], [7]). In this...
Yonggeun Cho, Gyeongha Hwang, Changhun Yang. Source: Advances in Differential Equations, Volume 23, Number 9/10, 649--692.Abstract: In this paper, we study 3-d Hartree type fractional Schrödinger equations: $$ i\partial_{t}u-\vert\nabla\vert^{\alpha}u = \lambda \left ( |x|^{-\gamma} *\vert...
Kanishka Perera, Cyril Tintarev, Jun Wang, Zhitao Zhang. Source: Advances in Differential Equations, Volume 23, Number 7/8, 615--648.Abstract: We study the existence of ground and bound state solutions for a system of coupled Schrödinger equations with linear and nonlinear couplings in...
Motohiro Sobajima, Yuta Wakasugi. Source: Advances in Differential Equations, Volume 23, Number 7/8, 581--614.Abstract: In this paper, we study the asymptotic behavior of solutions to the wave equation with damping depending on the space variable and growing at the spatial infinity. We prove that...
Abstract. The so-called "Japanese theorem" dates back over 200 years; in its original form it states that given a quadrilateral inscribed in a circle, the sum of the inradii of the two triangles formed by the addition of a diagonal does not depend on the choice of diagonal. Later it was shown that...
In the United States, congressional districts are redrawn every ten years based on changes in population revealed by the census. Individual states are responsible for redrawing their congressional districts. Often sophisticated (and expensive) software packages are used to guide redistricting...
This article analyzes the physical and mathematical properties of the mirascope and models the mirascope using dynamic learning technology
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This article explores analogues of the Pythagorean Theorem in non-Euclidean geometries.
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