On the uniqueness of solutions in inverse problems for Burgers’ equation under a transverse diffusion. (English) Zbl 1520.80002
Summary: We consider the inverse problems of restoring initial data and a source term depending on spatial variables and time in boundary value problems for the two-dimensional Burgers equation under a transverse diffusion in a rectangular and on a half-strip, like the Hopf-Cole transformation is applied to reduce Burgers’ equation to the heat equation with respect to the function that can be measured to obtain tomographic data. We prove the uniqueness of solutions in inverse problems with such additional data based on the Fourier representations and the Laplace transformation.
MSC:
| 80A23 | Inverse problems in thermodynamics and heat transfer |
| 44A10 | Laplace transform |
| 34B24 | Sturm-Liouville theory |
| 34L10 | Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators |
| 45D05 | Volterra integral equations |
| 35Q79 | PDEs in connection with classical thermodynamics and heat transfer |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35Q41 | Time-dependent Schrödinger equations and Dirac equations |
| 35R30 | Inverse problems for PDEs |
Keywords:
transverse diffusion; heat equation; Hopf-Cole transformation; tomographic data; Sturm-Liouville problem; Fourier and Laplace transformsReferences:
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