# A Stabilization Method for the Tricomi Problem

### N.A. Lar'kin

Institute for Theoretical and Applied Mechanics, Novosibirsk, Russian Federation### M. Schneider

Karlsruher Institut für Technologie (KIT), Germany

## Abstract

We prove the existence of a generalized solution of the Tricomi problem for the equation $L_{0}[u]=T[u]+λl(u):=yu_{zz}+u_{yy}+λ1(u)=f$, where $l=α_{1}∂/∂x+α_{2}∂/∂y$ is a special differential operator and $λ≥0$ is a constant. Then we show the solvability of an initial boundary value problem for the evolution equation $L[u]=T[u]+∂(u)/∂t=F$ by an aproximation method. It is shown that the generalized solution of the evolution problem converges to the generalized solution of the Tricomi problem $T[u]=f$ as $t→∞$. The rate of convergence is estimated.

## Cite this article

N.A. Lar'kin, M. Schneider, A Stabilization Method for the Tricomi Problem. Z. Anal. Anwend. 9 (1990), no. 3, pp. 193–202

DOI 10.4171/ZAA/394