. A thin wire coinciding with the x-axis on the interval [-L, L]is bent into the shape of a circle so that the ends xand x =L are joined. Under

certain conditions the temperature u(x, t) in the wire satisfies the boundary-value problem k \frac{\partial^{2} u}{\partial x^{2}}=\frac{\partial u}{\partial t},-L0 u(-L, t)=u(L, t), t>0 \left.\frac{\partial u}{\partial x}\right|_{x=-L}=\left.\frac{\partial u}{\partial x}\right|_{x=L}, t>0 u(x, 0)=f(x),-L