| 叶耀军,李兰兰.一类具有粘性项的拟线性抛物型方程组*[J].数学年刊A辑,2022,43(3):283~300 |
| 一类具有粘性项的拟线性抛物型方程组* |
| A Quasilinear Parabolic Systems with Viscoelastic Term |
| Received:January 16, 2021 Revised:January 24, 2022 |
| DOI：10.16205/j.cnki.cama.2022.0019 |
| 中文关键词: 拟线性抛物型方程组, 粘性项, 整体解, 爆破, 生命区间估计 |
| 英文关键词:Quasilinear parabolic systems, Viscoelastic terms, Global solutions, Blow-up, Lifespan estimates |
| 基金项目:浙江省自然科学基金 (No.LY17A010009) |
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| 中文摘要: |
| 研究了一类具有非线性源项和粘性项的拟线性抛物型方程组的初边值问题．通过构造稳定集, 证明了此问题整体解的存在性, 并建立了解的长时间行为．同时在放松函数的适当假设条件下, 得到了初始能量非负时解的爆破性质及解的生命区间估计． |
| 英文摘要: |
| The initial-boundary value problem for a class of quasilinear parabolic systems with viscoelastic terms and nonlinear source terms is studied. The existence of global solutions for this problem is proved by constructing a stable set, and the asymptotic behavior of the global solutions is establised. Meanwhile, under suitable conditions on relaxation function and the positive initial energy, the authors obtain blow-up result for some solutions and give the lifespan estimates of solutions. |
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