Pregled bibliografske jedinice broj: 719417
On the heat equation involving the δ-distribution as a coefficient
On the heat equation involving the δ-distribution as a coefficient // Mathematical and computer modelling, 50 (2009), 1/2; 109-115 doi:10.1016/j.mcm.2009.02.005 (međunarodna recenzija, članak, znanstveni)
CROSBI ID: 719417 Za ispravke kontaktirajte CROSBI podršku putem web obrasca
Naslov
On the heat equation involving the δ-distribution as a coefficient
Autori
Mitrović, Darko
Izvornik
Mathematical and computer modelling (0895-7177) 50
(2009), 1/2;
109-115
Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni
Ključne riječi
heat equation; singular coefficients; multiplication of distributions
Sažetak
We show existence of solution to the heat equation with the Dirac distribution as a coefficient. We consider the equation (aH(x+st)+bH(−x−st)+δ(x+st))ut(x, t)=uxx(x, t), where (x, t)∈R×R+, b, s∈R are fixed constants, HH is the Heaviside function, and δδ is the Dirac distribution. We augment the equation with appropriate initial and boundary data. We give a physical model justifying such an equation, and introduce a new solution concept with the help of a distribution space defined on discontinuous test functions. We prove the existence and uniqueness of a solution in the framework of the proposed solution concept.
Izvorni jezik
Engleski
Citiraj ovu publikaciju:
Časopis indeksira:
- Current Contents Connect (CCC)
- Web of Science Core Collection (WoSCC)
- Science Citation Index Expanded (SCI-EXP)
- SCI-EXP, SSCI i/ili A&HCI
- Scopus
Uključenost u ostale bibliografske baze podataka::
- Zentrallblatt für Mathematik/Mathematical Abstracts
