Non-linear parabolic problem associated with the penetration of a magnetic field into a substance

✍ Scribed by Nguyen Thanh Long; Pham Ngoc Dinh Alain

• Publisher: John Wiley and Sons
• Year: 1993
• Tongue: English
• Weight: 471 KB
• Volume: 16
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1670160404

✦ Synopsis

Abstract

We study the following initial and boundary value problem:
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In section 1, with u~0~ in L^2^(Ω), f continuous such that f(u) + ϵ non‐decreasing for ϵ positive, we prove the existence of a unique solution on (0,T), for each T > 0. In section 2 it is proved that the unique soluition u belongs to L^2^(0, T; H ∩ H^2^) ∩ L^∞^(0, T; H) if we assume u~0~ in H and f in C^1^(ℝ,ℝ). Numerical results are given for these two cases.