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The theory of non-stationary ion-acoustic waves in a non-magnetized plasma. (English. Russian original) Zbl 0842.76094
Comput. Math. Math. Phys. 35, No. 2, 247-252 (1995); translation from Zh. Vychisl. Mat. Mat. Fiz. 35, No. 2, 303-309 (1995).
Summary: The Cauchy problem for the two-dimensional equation of ion-acoustic waves in non-magnetized plasma $$D^2_t (\Delta_2 u- u)+ \Delta_2 u= f(x, t)$$, $$x\in \mathbb{R}^2$$, $$t\in \mathbb{R}^1$$ is investigated, where $$\Delta_2$$ is the Laplacian with respect to variables $$x_1$$ and $$x_2$$. Its explicit solution is constructed and its behaviour as $$t\to +\infty$$ is studied. In particular, the existence of steady oscillations is proved.
##### MSC:
 76X05 Ionized gas flow in electromagnetic fields; plasmic flow 35Q35 PDEs in connection with fluid mechanics