컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0483 |
|---|---|
| 분류(Section) | Contributed Talk |
| 분과(Session) | Partial Differential Equations (SS-11) |
| 영문제목 (Title(Eng.)) |
On the unique solvability of a class of first-order nonlinear partial differential equations |
| 저자(Author(s)) |
Jose Ernie C. Lope1, Marian P. Roque1, Hidetoshi Tahara2 Institute of Mathematics, University of the Philippines Diliman, Quezon City, Philippines1, Department of Mathematics, Sophia University, Tokyo, Japan2 |
| 초록본문(Abstract) | In this talk, we show the existence and uniqueness of the solution of a class of singular nonlinear partial differential equations of the form $$tu_{t}=F(t,x,u,u_{x}),$$ where the function $F$ is continuous in $t$ and holomorphic in the other variables. We assume some growth conditions on the coefficients of the partial Taylor expansion of $F$ and show that if $F(t,x,0,0)$ is of order $O(\mu(t)^{\alpha})$ for some $\alpha\in[0,1]$ as $t\rightarrow0$ uniformly in some neighborhood of $x=0$, then the equation has a unique solution $u(t,x)$ with the same growth order. |
| 분류기호 (MSC number(s)) |
35A10, 35A20, 35F20 |
| 키워드(Keyword(s)) | unique solvability, singular partial differential equations, weight function |
| 강연 형태 (Language of Session (Talk)) |
English |