摘要:

AbstractLetf(u) be twice continuously differentiable on [0,c]) for some constantcsuch thatf(0)>0,f′ ⩾ 0,f″ ⩾ 0, and limu→cf(u) = ∞. Also, let χ(S) be the characteristic function of the setS. This article studies all solutionsuwith non‐negativeut, in the region whereu

ISSN:0170-4214    

DOI:10.1002/mma.1670170102

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractThe physical model for penetrative convection in porous media is here considered to study the effects of variation of the source parameters on the flow. In this note we study the continuous dependence upon the heat supply and the body force of the classical solutions to the initial‐boundary value problem of a heat conducting fluid through a porous solid, both for the (well‐posed) forward problem and for the (improperly posed) backward in time one. For the former problem we obtain a result of continuous dependence with respect to theL2norm; while for the latter we prove a result of Hölder continuity in a suitably constrained class of solut

ISSN:0170-4214    

DOI:10.1002/mma.1670170103

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractWe study some boundary value problems on two‐dimensional polygonal topological networks, where on each face, the considered operator is the biharmonic operator. The transmission conditions we impose along the edges are inspired by the models introduced by H. Le Dret [13] and Destuynder and Nevers [9]. The boundary conditions on the external edges are the classical ones. This class of problem contains the boundary value problems for the biharmonic equation in a plane polygon (see [3, 11, 12, 18]). Conforming to the classical results cited above, we prove that the weak solution of our problem admits a decomposition into a regular part and a singular part, the latter being a linear combination of singular functions depending on the domain and the considered boundary value problem. Finally, we give the exact formula for the coefficients of these singularitie

ISSN:0170-4214    

DOI:10.1002/mma.1670170104

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractIn this paper, we investigate problems of approximation for the solution of a system of coupled semi‐linear parabolic partial differential equations that model diffusion‐reaction problems in chemical engineering. Given that the solutions belong toHs(0, ∞), we consider finite‐element approximations on bounded domains (0,R(h)) such that limh→0[R(h)] = ∞. Optimal convergence estimates are found to depend on the asymptotic behaviour of the solution and its regularity neart= 0. In theL2‐norm, they cannot exceed an order ofO((;h2/t3/4) +h2[Inh]2). For that purpose, a Wheeler‐type argument is also generalized to non‐coercive elliptic forms. Fully discrete schemes that preserve the positivity of the solutions are also considered. Due to the singularity att= 0, they lead to estimates of the ord

ISSN:0170-4214    

DOI:10.1002/mma.1670170105

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractIn this paper we construct two approximating sequences for heteroclinic solution to a scalar ODE. These sequences do not ‘intersect’ and bound a unique real solution from below and above, thus enabling us to estimate this solution with any accur

ISSN:0170-4214    

DOI:10.1002/mma.1670170106

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

ISSN:0170-4214    

DOI:10.1002/mma.1670170101

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY