𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On Time Periodic Solutions of the Dirichlet Problem for Degenerate Parabolic Equations of Nondivergence Type

✍ Scribed by Yoshikazu Giga; Noriko Mizoguchi

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
206 KB
Volume
201
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, we are concerned with the existence of periodic solutions of a quasilinear parabolic equation

t with the Dirichlet boundary condition, where ⍀ is a smoothly bounded domain in N R and f is a given function periodic in time defined on ⍀ = R. Our results depend on the first eigenvalue of y⌬ in ⍀ with the Dirichlet boundary 1 condition. If ) 1, then there exists a unique positive periodic solution for a 1 Ε½ . positive f β₯ g R . In the case of -1, we construct a nonnegative periodic 1 Ε½

. solution for a negative f 1 F β₯ -3 .

πŸ“œ SIMILAR VOLUMES

On the Existence of Periodic Solutions f
On the Existence of Periodic Solutions for a Certain Type of Nonlinear Differential Equations
✍ M. Feckan πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 359 KB

Bifurcations of periodic solutions are studied for certain types of weakly perturbed partial differential equations. It is shown that a bifurcation occurs for almost all (in the sense of the Lebesque measure) periodic small perturbations. A generalized implicit function theorem is applied. (" 1995 A

Solvability of the Tricomi problem for s
Solvability of the Tricomi problem for second order equations of mixed type with degenerate curve on the sides of an angle
✍ Guo Chun Wen πŸ“‚ Article πŸ“… 2008 πŸ› John Wiley and Sons 🌐 English βš– 210 KB

## Abstract In [1]–[6], the author posed and discussed the Tricomi problem of second order mixed equations, but he only consider some special mixed equations. In [3], the author discussed the uniqueness of solutions of the Tricomi problem for some second order mixed equation with nonsmooth degenera