An Existence Proof for a Problem in Singular Parabolic Partial Differential Equations
James F. Scott · IMA Journal of Applied Mathematics · 1980
In a previous paper (Crighton & Scott, 1979) it was shown how the method of matched asymptotic expansions applied to a problem of non-linear acoustics leads to a parabolic equation with asymptotic initial conditions. To ensure that the scalings used are correct it is necessary to prove the existence of a solution to this problem. In the present paper we demonstrate existence and in so doing we also obtain some bounds on the solution.