Global solutions for quasilinear parabolic systems
نویسندگان
چکیده
منابع مشابه
Classical solutions of quasilinear parabolic systems on two dimensional domains
Using a classical theorem of Sobolevskii on equations of parabolic type in a Banach space and recently obtained results on elliptic operators with discontinuous coefficients including mixed boundary conditions we prove that quasilinear parabolic systems in diagonal form admit a local, classical solution in the space of p–integrable functions, for some p > 1, over a bounded two dimensional space...
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Abstract. We bound the difference between solutions u and v of ut = a∆u+ divx f + h and vt = b∆v + divx g + k with initial data φ and ψ, respectively, by ‖u(t, ·)− v(t, ·)‖Lp(E) ≤ AE(t)‖φ−ψ‖ 2ρp L∞(Rn) +B(t)(‖a− b‖∞ + ‖∇x · f − ∇x · g‖∞ + ‖fu − gu‖∞ + ‖h− k‖∞)p |E| ηp . Here all functions a, f , and h are smooth and bounded, and may depend on u, x ∈ R, and t. The functions a and h may in additi...
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متن کاملGlobal Existence and L∞ Estimates of Solutions for a Quasilinear Parabolic System
ut = ∇ · (|∇u|m∇u) + f(u, v), x ∈ Ω, t > 0, vt = ∇ · (|∇v|n∇v) + g(u, v), x ∈ Ω, t > 0, (1.1) u(x, 0) = u0(x), v(x, 0) = v0(x), x ∈ Ω, u(x, t) = v(x, t) = 0, x ∈ ∂Ω, where Ω is a bounded domain in R(N > 1) with smooth boundary ∂Ω and m,n > 0. For m = n = 0, f(u, v) = uv, g(u, v) = uv and u0(x), v0(x) ≥ 0, the problem (1.1) has been investigated extensively and the existence and nonexistence of ...
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Article history: Received 9 July 2008 Revised 23 October 2008 Available online 9 December 2008 MSC: 34G20 35K55 35B35 37D10 35R35
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2004
ISSN: 0022-0396
DOI: 10.1016/s0022-0396(03)00165-7