Decay of nonnegative solutions of singular parabolic equations with KPZ-nonlinearities
A. B. Muravnikab
a Joint Stock Company "Concern "Sozvesdie"
b RUDN University, Moscow, 117198 Russia
The Cauchy problem for quasilinear parabolic equations with KPZ-nonlinearities is considered. It is proved that the behavior of the solution as
$t\to\infty$ can change substantially as compared with the homogeneous case if the equation involves zero-order terms. More specifically, the solution decays at infinity irrespective of the behavior of the initial function and the rate and character of this decay depend on the conditions imposed on the lower order coefficients of the equation.
parabolic equations, quasilinear equations, KPZ-nonlinearities, lower-order terms, behavior at infinity.
|This work was supported by the Russian Foundation for Basic Research (project no. 20-01-00288 A) (Theorems 1, 2) and by the RUDN program “5-100” (Theorems 3, 4).
Computational Mathematics and Mathematical Physics, 2020, 60:8, 1375–1380
A. B. Muravnik, “Decay of nonnegative solutions of singular parabolic equations with KPZ-nonlinearities”, Zh. Vychisl. Mat. Mat. Fiz., 60:8 (2020), 1422–1427; Comput. Math. Math. Phys., 60:8 (2020), 1375–1380
Citation in format AMSBIB
\paper Decay of nonnegative solutions of singular parabolic equations with KPZ-nonlinearities
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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