Abstract
In this paper, we establish maximal Lp-Lq estimates for rum-autonomous parabolic equations of the type u′(t) + A(t)u(t) = f(t), u(0) = 0 under suitable conditions on the kernels of the semigroups generated by the operators -A(t), t ∈ [0, T]. We apply this result on semilinear problems of the form u′(t) + A(t)u(t) = f(t, u(t)), u(0) = 0.
| Original language | English |
|---|---|
| Pages (from-to) | 467-481 |
| Number of pages | 15 |
| Journal | Journal of Fourier Analysis and Applications |
| Volume | 6 |
| Issue number | 5 |
| Publication status | Published - 2000 |
| Externally published | Yes |
Keywords
- Heat-kernel estimates
- Maximal L - L- Regularity
- Non-autonomous cauchy problem
- Singular integrals
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
- Analysis