| 詹华税,袁洪君.关于具有阻尼项的扩散方程[J].数学年刊A辑,2021,42(2):189~200 |
| 关于具有阻尼项的扩散方程 |
| On a Diffusion Equation with a Damping Term |
| Received:September 25, 2018 Revised:March 11, 2019 |
| DOI：10.16205/j.cnki.cama.2021.0016 |
| 中文关键词: 弱解, 阻尼项, 初边值问题, 唯一性 |
| 英文关键词:Week solution, Damping term, Initial-boundary value problem,Uniqueness |
| 基金项目:福建省自然科学基金 (No.,2019J01858) |
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| 中文摘要: |
| 讨论了该方程的初边值问题解的存在性, 其中alpha>0, q |
| 英文摘要: |
| The authors study diffusion equation with a damping term ?u ?t = div(ρα|?u|p?2?u) ? a(x)|?u|q ,where α > 0, q < p, ρ(x) = dist(x, ??) is the distance function from the boundary ??, a(x)is a nonnegative bounded function. By the parabolic regularized method, the existence of the weak solution is obtained. By choosing a suitable test function, the uniqueness of the weak solution is proved without any boundary value condition. |
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