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The evolution equation for finite amplitude acoustic waves in a relaxing medium is usually analyzed approximately or numerically. Attempts to find exact solutions to that equation using different approaches including classical and non-classical symmetries and conservation laws are described in this work. All obtained solutions are essentially non-limited in the space coordinate, and this fact had led to the proposition that validity of the initial equation in the general case should be revised. A correction of the evolution equation is proposed in the present work, and solutions in the form of weak shocks are derived for different boundary conditions.