Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Existence of classical solutions for singular parabolic problems


Authors: C. Y. Chan and Benedict M. Wong
Journal: Quart. Appl. Math. 53 (1995), 201-213
MSC: Primary 35K20; Secondary 35K65
DOI: https://doi.org/10.1090/qam/1330648
MathSciNet review: MR1330648
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ Lu \equiv {u_{xx}} + b{u_x}/x - {u_t}$ with $ b$ a constant less than 1. Its Green's function corresponding to first boundary conditions is constructed by eigenfunction expansion. With this, a representation formula is established to obtain existence of a classical solution for the linear first initial-boundary value problem. Uniqueness of a solution follows from the strong maximum principle. Properties of Green's function and of the solution are also investigated.


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Additional Information

DOI: https://doi.org/10.1090/qam/1330648
Article copyright: © Copyright 1995 American Mathematical Society

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