A. Shishkov

activity

20072009

most citedOn convergence in smooth gradient systems with branching of equilibria

1 citations · 1 across the 6 of their papers we have counts for

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math.AP2009

Extinction of solutions of semilinear higher order parabolic equations with degenerate absorption potential

Yves Belaud, Andrey Shishkov

We study the first vanishing time for solutions of the Cauchy-Dirichlet problem to the semilinear $2 m$ -order ( $m \geq 1$ ) parabolic equation $u_{t} + Lu + a (x) ∣ u ∣^{q - 1} u = 0$ , $0 < q < 1$ wit…

math.AP2009★ 1 cited

On convergence in smooth gradient systems with branching of equilibria

V. A. Galaktionov, S. I. Pohozaev, A. E. Shishkov

T.I. Zelenyak's ideas and method of 1968 are shown to apply to N-dimensional second- and higher-order parabolic equtions and ensure a fast exponential convergence to degenerate equ…

math.AP2008

The balance between diffusion and absorption in semilinear parabolic equations

Andrey Shishkov, Laurent Veron

Let $h : [0, \infty) \mapsto [0, \infty)$ be continuous and nondecreasing, $h (t) > 0$ if $t > 0$ , and $m, q$ be positive real numbers. We investigate the behavior when $k \to \infty$ of the fu…

math.AP2008

Diffusion versus absorption in semilinear parabolic equations

Andrey Shishkov, Laurent Veron

We study the limit, when $k \to \infty$ , of the solutions $u = u_{k}$ of (E) $\prt_{t}u-Δu+ h(t)u^q=0$ in $\BBR^N\ti (0,\infty)$, $u_{k} (., 0) = k δ_{0}$ , with $q > 1$ , $h (t) > 0$ . If $h(t)=e^…

math.AP2008

Long-time extinction of solutions of some semilinear parabolic equations

Yves Belaud, Andrey Shishkov

We study the long time behaviour of solutions of semi-linear parabolic equation of the following type $\partial_{t} u - Δ u + a_{0} (x) u^{q} = 0$ where $a_0(x) \geq d_0 \exp(\frac{ω(|x|)}{|x|^2}…

math.AP2007

Singular solutions of some nonlinear parabolic equations with spatially inhomogeneous absorption

Andrey Shishkov, Laurent Veron

We study the limit behaviour of solutions of a class of solutions of nonlinear parabolic equations with a degenerate strong absorption. We prove that two types of phenomena can occ…