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Boundary value controllability and observability problems for the wave and heat equation
| Content Provider | Scilit |
|---|---|
| Author | Werner, K. -D. |
| Copyright Year | 1988 |
| Description | In this paper, we study controllability and observability problems for the wave and heat equation in a spherical region in $R^{n}$, where the control enters in the mixed boundary condition. In the main result, we show that all “finite energy” initial states (i.e. $(ω_{0}$, $ν_{0}$) ∈ $H^{1}$(Ω) × $L^{2}$ (Ω)) can be steered to zero at time T, using a control f ∈ $L^{2}$ (∂Ω × [0, T]), provided T > 2. On this basis, we use the duality principle to investigate initial observability for the wave equation. Applying the Fourier transform technique, we obtain controllability and observability results for the heat equation. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/DFD69417BF4802FAB0B6579266E0146C/S0334270000005956a.pdf/div-class-title-boundary-value-controllability-and-observability-problems-for-the-wave-and-heat-equation-div.pdf |
| Ending Page | 479 |
| Page Count | 19 |
| Starting Page | 461 |
| ISSN | 03342700 |
| e-ISSN | 18394078 |
| DOI | 10.1017/s0334270000005956 |
| Journal | The Journal of the Australian Mathematical Society. Series B. Applied Mathematics |
| Issue Number | 4 |
| Volume Number | 29 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1988-04-01 |
| Access Restriction | Open |
| Subject Keyword | The Journal of the Australian Mathematical Society. Series B. Applied Mathematics Applied Mathematics Heat Equation |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
