论文标题
一维热弹性的模型
A model in one-dimensional thermoelasticity
论文作者
论文摘要
我们研究了热弹性理论中出现的一维非线性双曲线 - 羟基寄生虫初始边界值问题。我们证明了局部强大解决方案的存在和独特性。同样，某些全球时间较弱的衡量解决方案也被证明存在。为此，我们引入了人工粘度的辅助问题，并证明了其全球及时的适应性。接下来，我们表明辅助问题的解决方案会在某个短时间间隔间隔到强解决方案，并在任意时间内与我们的度量有价值的解决方案相聚。
We study a one-dimensional nonlinear hyperbolic-parabolic initial boundary value problem occurring in the theory of thermoelasticity. We prove existence and uniqueness of the local-in-time strong solution. Also, some global-in-time weak measure valued solutions are proven to exist. To this end we introduce an auxiliary problem with artificial viscosity and prove its global-in-time well-posedness. Next, we show that solutions of the auxiliary problem converge, at some short time interval to the strong solution, and to our measure valued solution for an arbitrary time.
