一類(lèi)帶記憶項(xiàng)的波動(dòng)方程解的破裂

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【摘   要】   在[n]維空間中研究一類(lèi)帶散射阻尼項(xiàng)和記憶項(xiàng)的半線(xiàn)性波動(dòng)方程的柯西問(wèn)題。通過(guò)引入乘子處理阻尼項(xiàng)，構(gòu)造檢驗(yàn)函數(shù)，并且利用迭代方法，得到當(dāng)非線(xiàn)性項(xiàng)指數(shù)滿(mǎn)足一定條件時(shí)，問(wèn)題的解會(huì)在有限時(shí)間內(nèi)破裂，并給出解的生命跨度的上界估計(jì)。

【關(guān)鍵詞】   波動(dòng)方程；記憶項(xiàng)；迭代方法；破裂；生命跨度估計(jì)

Blow-up of Solutions for a Class of Wave Equations with Memory Term

Xue Hui1， Ming Sen2

（1.Shanxi Finance & Taxation College， Taiyuan 030024， China；

2.North University of China， Taiyuan 030051， China）

【Abstract】    This paper is concerned with the study of Cauchy problem for the nonlinear wave equation with scattering damping term and memory term for [n]space dimensions. Blow-up of solution in finite time is proved under a certain assumption for the exponent in nonlinear term. By introducing a multiplier to deal with the damping term， constructing a test function and using iteration method， the author obtains upper bound lifespan estimate of solution for the problem.

【Key words】     wave equation; memory term; iteration method; blow-up; lifespan estimate

〔中圖分類(lèi)號(hào)〕 O175.29                   〔文獻(xiàn)標(biāo)識(shí)碼〕  A              〔文章編號(hào)〕 1674 - 3229（2024）03 - 0021 - 04

0     引言

近年來(lái)，非線(xiàn)性波動(dòng)方程的柯西問(wèn)題和初邊值問(wèn)題引起廣泛關(guān)注［1-7］，即探究問(wèn)題解破裂時(shí)生命跨度的上界估計(jì)、非線(xiàn)性項(xiàng)指數(shù)和空間維數(shù)三者之間的關(guān)系。（剩余5570字）