Identification of an unknown spatial source function in a multidimensional hyperbolic partial differential equation with interior degeneracy

Numerical Recovering of Space-Dependent Sources in Hyperbolic Transmission Problems

“…Inverse source problems in wave propagations in a single domain are well studied (see, e.g., [13,15,17,21,22]). In contrast, there are no results in the literature for inverse hyperbolic problems on separate intervals.…”

“…In addition, the solution may be unstable [10][11][12][13][14]. The ill-posedness is usually overcome by using regularization methods [10,12,[14][15][16][17]. Another often used approach is to transform the inverse problem to a well-posed direct problem [14,[18][19][20].…”

“…Recently, many investigations have been devoted to inverse problems for PDEs, in particular, inverse problems for hyperbolic-type equations. Inverse problems for HPDEs in the connected domain are well studied in the literature (see, e.g., [13,15,17,21] and references therein).…”

“…A boundary control method is utilized in [21] to solve the inverse coefficient problem for wave equations. The identification of the spatial part of the source term of a degenerate wave equation based on the final observation data is studied in [17]. The inverse problem is formulated as a nonlinear optimization problem.…”

“…The motivation is explained by the capacity of the hyperbolic equations to describe a large number of problems in elasticity, thermoelasticity and wave propagation (see, e.g., [2][3][4][5][6]12,18,22]). Also, it comes from the theoretical and numerical challenges of the present specific problem (see, e.g., [5,[8][9][10][11][12]15,17,18,21,23]).…”