Dirichlet problem in the ball for an equation with a delta-like coefficient
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
We study the Dirichlet problem in the ball for the Helmholtz equation with an additional term in the form of the product by the delta function. The additional term is approximated by the simplest integral expression, and the solution of the original equation is defined as the limit of solutions of the regularized equations. We obtain exact solutions depending on the chosen method of approximation.
- Albeverio, S., Gesztesy, F., Høegh-Krohn, R., and Holden, H., Solvable Models in Quantum Mechanics, Berlin: Springer, 1988. Translated under the title Reshaemye modeli v kvantovoi mekhanike, Moscow, 1991. CrossRef
- Antonevich, A.B. and Romanchuk, T.A., Approximations of Operators with Delta-Like Coefficients, in Aktual’nye problemy matematiki, Sb. nauch. trudov GrGU im Ya. Kupaly (Topical Problems of Mathematics. Collection of Scientific Papers of the Grodno State University), Grodno, 2008, pp. 11–28.
- Il’in, D.V., Stationary Schrödinger Operator with δ-Potential: the Method of Finite-Dimensional Perturbations, Cand. Sci. (Phys.-Math.) Dissertation, Minsk, 2000.
- Tikhonov, A.N. and Samarskii, A.A., Uravneniya matematicheskoi fiziki (Equations of Mathematical Physics), Moscow, 2004.
- Vladimirov, V.S., Uravneniya matematicheskoi fiziki (Equations of Mathematical Physics), Moscow: Nauka, 1988.
- Lyusternik, L.A. and Sobolev, V.I., Elementy funktsional’nogo analiza (Elements of Functional Analysis), Moscow: Nauka, 1965.
- Dirichlet problem in the ball for an equation with a delta-like coefficient
Volume 48, Issue 8 , pp 1119-1126
- Cover Date
- Print ISSN
- Online ISSN
- SP MAIK Nauka/Interperiodica
- Additional Links