Computational methods for time-periodic solutions of singular semilinear parabolic problems
โ Scribed by C.Y. Chan; Benedict M. Wong
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 929 KB
- Volume
- 42
- Category
- Article
- ISSN
- 0096-3003
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๐ SIMILAR VOLUMES
## Abstract Theoretical aspects related to the approximation of the semilinear parabolic equation: $u\_t=\Delta u+f(u)$\nopagenumbers\end, with a finite unknown โblowโupโ time __T__~b~ have been studied in a previous work. Specifically, for __ฮต__ a small positive number, we have considered coupled
where p > 1, ฮต > 0, is a bounded domain in R N , and ฯ is a continuous function on . It is shown that the blowup time T ฮต of the solution of this problem satisfies T ฮต โ 1 p-1 ฯ 1-p โ as ฮต โ 0. Moreover, when the maximum of ฯ x is attained at one point, we determine the higher order term of T ฮต whic
In this paper, we are concerned with the existence of periodic solutions of a quasilinear parabolic equation t with the Dirichlet boundary condition, where โ is a smoothly bounded domain in N R and f is a given function periodic in time defined on โ = R. Our results depend on the first eigenvalue o
We consider a very general second order nonlinear parabolic boundary value problem. Assuming the existence of an upper solution . and a lower solution satisfying ., we show that the problem has extremal periodic solutions in the order interval K=[ , .]. Our proof is based on a general surjectivity