论文标题
描述非线性Timoshenko光束的非自主变异问题
A non-autonomous variational problem describing a nonlinear Timoshenko beam
论文作者
论文摘要
我们研究了非自主变异问题： \ begin {equation*} \ inf _ {（ϕ，θ）} \ bigg \ {\ int_0^1 \ bigG（\ frac {k} {2} ϕ'^2 + \ frac {（ϕ-θ）^2} {2} -v（x，θ）\ bigg）\ text {d} x \ bigg \} \ end {equation*} 其中$ k> 0 $，$ v $是一个有限的连续功能， $（ϕ，θ）\ in H^1（[0,1]）\ times l^2（[0,1]）$和$ ϕ（0）= 0 $ 从痕迹的意义上讲。该问题的特殊性是在不同规律性顺序的空间产品中设置其设置。这种形式的问题是在弹性静力学中出现的，当研究分布载荷下的非线性timoshenko梁的平衡和经典动力学 在延时的外场中的耦合粒子的粒子。我们证明了全球最小化器和研究的存在和定性属性，并在$ v $的其他假设下，当地最小化器的存在和规律性。
We study the non-autonomous variational problem: \begin{equation*} \inf_{(ϕ,θ)} \bigg\{\int_0^1 \bigg(\frac{k}{2}ϕ'^2 + \frac{(ϕ-θ)^2}{2}-V(x,θ)\bigg)\text{d}x\bigg\} \end{equation*} where $k>0$, $V$ is a bounded continuous function, $(ϕ,θ)\in H^1([0,1])\times L^2([0,1])$ and $ϕ(0)=0$ in the sense of traces. The peculiarity of the problem is its setting in the product of spaces of different regularity order. Problems with this form arise in elastostatics, when studying the equilibria of a nonlinear Timoshenko beam under distributed load, and in classical dynamics of coupled particles in time-depending external fields. We prove the existence and qualitative properties of global minimizers and study, under additional assumptions on $V$, the existence and regularity of local minimizers.
