7 月 3 日 (金) 16:30 - 17:30
場所: 北海道大学 理学部 4 号館 4-501
講演者: Bushra Nisar (北海道大学)
タイトル: Global Weak Solutions to the nonlinear Wave Equation with Damping under Fractional Derivative Control
▶ アブストラクト
In this talk, I will discuss a nonlinear wave equation with fractional-order boundary damping, nonlinear damping, and a nonlinear source term. The fractional boundary condition introduces significant analytical difficulties and prevents a direct application of standard existence theories. To overcome this difficulty, we extend the spatial domain by a symmetry argument and reformulate the fractional boundary condition through an augmented system. Weak solutions to the extended problem are then constructed by means of the Galerkin method, and solutions to the original problem are recovered using the symmetry of the extension. Finally, under suitable assumptions on the nonlinear source term and the initial data, we establish both local and global existence results for weak solutions by deriving appropriate energy estimates and applying a blow-up alternative argument. This is a joint work with Professor Hideo Kubo.