Channel flow of a viscous fluid in the boundary layer

A splitting moving mesh method for reaction–diffusion equations of quenching type

“…The initial temperature u 0 P 0 and is usually very small (it is thus usually assumed to be zero). The function /(x, y) represents certain singularity in the temperature transportation speed which causes the degeneracy in the differential equation (2.1) (see [10,15,28] for more details). The solution u of (2.1), (2.2) is said to quench if there exists a finite time T such that supfju t ðx; y; tÞj : ðx; yÞ 2 Dg !…”

A Rothe-Immersed Interface Method for a Class of Parabolic Interface Problems

“…The magnitude of the jump typically depends on the concentration. Similar processes are also observed in biological systems, on chemically active membranes, [1], [2], [10] and processes in which the ignition of a combustible medium is accomplished through the use of either a heated wire or a pair of small electrodes to supply a large amount of energy to a very confined area, [3].…”

Single-point blow-up for a degenerate parabolic problem due to a concentrated nonlinear source

“…By the principle of mathematical induction, i> <U1<U2<---< un-i < un in (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16) for any positive integer n.…”

“…When q = 1, the model may also be used to describe the temperature u of the channel flow of a fluid with temperature-dependent viscosity in the boundary layer (cf. Chan and Kong [2]) with a concentrated nonlinear source at /? ; here, and 7 denote the coordinates perpendicular and parallel to the channel wall respectively.…”