Next, we study the bi-Laplacian and associated equations: the iterated Poisson equation, the bi-Laplace Neumann and Dirichlet problems, and the "plate equation". It turns out that the bi-Laplace Dirichlet to Neumann map is of non-trivial interest. The exposition concludes with two detailed ...
Oscillatory properties of solutions to a class of second order damped partial differential equations with high order Laplace operator are studied. 研究一类含高阶Laplace算子的二阶阻尼偏微分方程解的振动性,通过利用Riccati变换、引入参数函数,获得该类方程在Robin、Dirichlet边值条件下振动的充分判据。 更多例句...
Blow-up scaling and global behaviour of solutions of the bi-Laplace equation in domains via pencil operators 喜欢 0 阅读量: 29 作者: VA Galaktionov,Pablo Álvarez-Caudevilla 摘要: As the main problem, the bi-Laplace equation \\begin{eqnarray} \\Delta^2 u=0 \\quad (\\Delta=D_...
On any bounded domain the Dirichlet or Neumann–Laplace operator has a first eigenfunction which is the unique one of fixed sign. For the bilaplace operator, as for any fourth order operator, there is no direct maximum principle and hence no obvious argument for a first eigenfunction of one ...
Bicomplex NumberLaplace Transform for complex variableROCIn this paper we have studied the bicomplex version of Laplace Transformation (LT), condition of existence and examined the Region of Convergence (ROC) of bicomplex Laplace Transformation geometrically with the help of projection on hyperbolic ...
Its proof requires the introduction of an appropriate semi-classical calculus and a delicate microlocal argument.doi:10.1023/A:1012477708874Jérôme Le RousseauLuc RobbianoA spectral inequality for the bi-laplace operator, preprint (2015), 48 pages....
bi-Laplace operatorCarleman estimatethree-ball inequalityunique continuationIn this paper, we prove a three-ball inequality for y satisfying an equation of the formFu, XiaoyuLiao, ZhonghuaSichuan Univ Sch Math Chengdu 610064 Peoples R ChinaMathematical Methods in the Applied Sciences...
Laplace TransformsGeneralized FunctionsUltrahyperbolic OperatorsLet $f(z, \\lambda), z\\in {\\open C}$ , be an entire function of the variables $z, \\lambda, f(z, \\lambda) = \\sum_{u = 0}^\\infty a_u(\\lambda)z^u$ . Let us consider the family of distributions of the ...
In addition, we derive an implicit upper bound for the nodal sets of solutions. We show two types of doubling inequalities for the solutions of bi-Laplace equations. As a consequence, the rate of vanishing is given for the solutions.doi:10.1007/s00205-018-01349-2Jiuyi Zhu...
bi‐Laplace operatorCarleman estimatethree‐ball inequalityunique continuationIn this paper, we prove a three‐ball inequality for y satisfying an equation of the form Δ 2 y = V 0 y + V 1 · y + V 2 Δ y + V 3 · Δ y in some open, connected set Ω of R n with V 0 , V...