On equations of evolution and parabolic equations of higher order in t
نویسندگان
چکیده
منابع مشابه
Nonlocal higher order evolution equations
In this paper we study the asymptotic behavior of solutions to the nonlocal operator ut(x, t) = (−1) n−1 (J ∗ Id − 1)n (u(x, t)), x ∈ R which is the nonlocal analogous to the higher order local evolution equation vt = (−1)(∆)v. We prove that solutions to both equations have the same asymptotic decay rate as t goes to infinity. Moreover, we prove that the solutions of the nonlocal problem conver...
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We consider a higher-order semilinear parabolic equationut =−(−∆)mu−g(x,u) in RN×R+, m>1. The nonlinear term is homogeneous: g(x,su)≡ |s|P−1sg(x,u) and g(sx,u) ≡ |s|Qg(x,u) for any s ∈ R, with exponents P > 1, and Q > −2m. We also assume that g satisfies necessary coercivity and monotonicity conditions for global existence of solutions with sufficiently small initial data. The equation is invar...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1970
ISSN: 0022-247X
DOI: 10.1016/0022-247x(70)90316-1