Self-similar grooving solutions to the Mullins’ equation
نویسندگان
چکیده
منابع مشابه
Self-similar solutions to a coagulation equation
The existence of self-similar solutions with a finite first moment is established for the Oort-Hulst-Safronov coagulation equation when the coagulation kernel is given by a(y, y∗) = yλ + yλ ∗ for some λ ∈ (0, 1). The corresponding self-similar profiles are compactly supported and have a discontinuity at the edge of their support. MSC 2000: 45K05, 45M05, 82C21
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Existence of self-similar solutions to the Oort-Hulst-Safronov coagulation equation with multiplicative coagulation kernel is established. These solutions are given by s(t)−τ ψτ (y/s(t)) for (t, y) ∈ (0, T )×(0,∞), where T is some arbitrary positive real number, s(t) = ((3−τ)(T − t))−1/(3−τ) and the parameter τ ranges in a given interval [τc, 3). In addition, the second moment of these self-sim...
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This paper discusses the diffusion equation with a damping term as follows ut = div(|Dum|p−2Dum)− u1 |Du|1 , where p > 2,m > 1, and p > p1, q1+p1m > m(p−1) > 1. By the standard Picard iteration method, a sufficient condition is given to the existence of the singular self-similar solutions. Moreover, the paper gives a classification for these singular self-similar solutions. Key–Words: Diffusion...
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ژورنال
عنوان ژورنال: Quarterly of Applied Mathematics
سال: 2020
ISSN: 0033-569X,1552-4485
DOI: 10.1090/qam/1570