Date of Award
1996
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
First Advisor
Jerome A. Goldstein
Abstract
In the dissertation, the generalized Kompaneets equation$${\partial u\over\partial t}={1\over\beta(x)}\lbrack\alpha(x)(u\sb{x}+ku+F(x,u))\rbrack\sb{x}$$(for $x,t>0)$ is studied. For the linear case, when $F\equiv0,$ a complete theory is given. A brief discussion is carried for the nonlinear case when $F(x,u)=f(x)g(u).$. For the following equation,$$v\sb{t}=\varphi(y,v\sb{y})v\sb{yy}+\psi(y,v,v\sb{y}),$$Goldstein and Lin's result is extended to degenerate case. Also, for the following linear operator,$$Au=\alpha(x)u\prime\prime+\beta(x)u\prime$$(for $x\in \lbrack 0,$ 1)), Clement and Timmermans' result is extended to the case of discontinuous coefficients $\alpha$ and $\beta$.
Recommended Citation
Wang, Kunyang, "The Generalized Kompaneets Equation." (1996). LSU Historical Dissertations and Theses. 6222.
https://repository.lsu.edu/gradschool_disstheses/6222
ISBN
9780591035490
Pages
57
DOI
10.31390/gradschool_disstheses.6222