The Burgers equation on the semiline with general boundary conditions at the origin.
In: Journal of Mathematical Physics, Jg. 32 (1991), Heft 1, S. 99-105
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Zugriff:
A technique is given to solve the initial/boundary value problem for the Burgers equation ut(x,t)=uxx(x,t)+2 ux(x,t) u(x,t) on the semiline 0≤x<∞, with the general boundary condition at the origin H[u(0,t),ux(0,t);t]=0. Here ‘‘to solve’’ means ‘‘to reduce to an equation in one variable only.’’ This equation is generally nonlinear and integrodifferent ial; it comes in several (equivalent) avatars, which contain nontrivially a free parameter, whose value can be assigned arbitrarily since the solution of the equation is independent of it. In the special case when H(y,z;t)=a(t)y+b(t)(z+y2) -F(t), which is the case relevant for most applications, the equations reduce to linear integral equations of Volterra type, which can in fact be solved by quadratures if a(t)/F(t)=c1 and b(t)/F(t)=c2 are time-independent. [ABSTRACT FROM AUTHOR]
Titel: |
The Burgers equation on the semiline with general boundary conditions at the origin.
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Autor/in / Beteiligte Person: | Calogero, F. ; De Lillo, S. |
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Zeitschrift: | Journal of Mathematical Physics, Jg. 32 (1991), Heft 1, S. 99-105 |
Veröffentlichung: | 1991 |
Medientyp: | academicJournal |
ISSN: | 0022-2488 (print) |
DOI: | 10.1063/1.529101 |
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