Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
842189 | Nonlinear Analysis: Theory, Methods & Applications | 2009 | 9 Pages |
Abstract
In this paper, we consider the local existence of solutions to the Cauchy problems for the following nonlinear evolution equations with mixed types {Ït=â(1âα)Ïâθx+αÏxx,θt=â(1âα)θ+γÏx+2Ïθx+αθxx, with initial data (Ï,θ)(x,0)=(Ï0(x),θ0(x))â(ϱ,θ±),as xâ±â, where α and γ are positive constants satisfying α<1, γ<α(1âα). Through constructing an approximation solution sequence, we obtain the local existence by using the contraction mapping principle.
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Authors
Hu Wei, Mina Jiang,