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Nonlinear diffusion equations with perturbation terms on unbounded domains

Kurima, Shunsuke (2017)

Proceedings of Equadiff 14

This paper considers the initial-boundary value problem for the nonlinear diffusion equation with the perturbation term u t + ( - Δ + 1 ) β ( u ) + G ( u ) = g in Ω × ( 0 , T ) in an unbounded domain Ω N with smooth bounded boundary, where N , T > 0 , β , is a single-valued maximal monotone function on , e.g., β ( r ) = | r | q - 1 r ( q > 0 , q 1 ) and G is a function on which can be regarded as a Lipschitz continuous operator from ( H 1 ( Ω ) ) * to ( H 1 ( Ω ) ) * . The present work establishes existence and estimates for the above problem.

Numerical study on the blow-up rate to a quasilinear parabolic equation

Anada, Koichi, Ishiwata, Tetsuya, Ushijima, Takeo (2017)

Proceedings of Equadiff 14

In this paper, we consider the blow-up solutions for a quasilinear parabolic partial differential equation u t = u 2 ( u x x + u ) . We numerically investigate the blow-up rates of these solutions by using a numerical method which is recently proposed by the authors [3].

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