Exact behavior of singular solutions to Protter's problem with lower order terms

Electronic Journal of Differential Equations

关键词: Wave equation;    boundary value problems;    generalized solutions;    singular solutions;    propagation of singularities;   

DOI  :  

来源: DOAJ

【 摘 要 】

For the (2+1)-D wave equation Protter formulated (1952) some boundaryvalue problems which are three-dimensional analogues of the Darbouxproblems on the plane. Protter studied these problems in a 3-D domain,bounded by two characteristic cones and by a planar region. Now it iswell known that, for an infinite number of smooth functions in theright-hand side, these problems do not have classical solutions, because ofthe strong power-type singularity which appears in the generalizedsolution. In the present paper we consider the wave equation involvinglower order terms and obtain new a priori estimates describing the exactbehavior of singular solutions of the third boundary value problem.According to the new estimates their singularity is of the same order as incase of the wave equation without lower order terms.

【 授权许可】

Unknown