ISSN:
0945-3245
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary The Cauchy problemu t =f(x, t, u, u x , u xx ),u(x, o)=ϕ(x),xεR, is treated with the longitudinal method of lines. Existence, uniqueness, monotonicity and convergence properties of the line method approximations are investigated under the classical assumption that ϕ satisfies an inequality |ϕ(x)|〈=conste Bx 2 . We obtain generalizations of the works of Kamynin [4], who got similar results in the case of the one dimensional heat equation when ϕ is allowed to grow likee Bx 2−δ, δ〉0, and of Walter [11], who proved convergence in the case of nonlinear parabolic differential equations under the growth condition |ϕ(x)|〈=conste B |x|
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01409988
Permalink