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Zbl 0798.35076
Deng, Keng
Exponential decay of solutions of semilinear parabolic equations with nonlocal initial conditions. (English)
[J] J. Math. Anal. Appl. 179, No.2, 630-637 (1993). ISSN 0022-247X

The nonlocal initial boundary value problem $$\aligned Lu+ g(x,t,u) & = 0,\quad x\in \Omega,\quad t>0,\\ u(x,t) & = 0,\quad x\in \partial\Omega,\quad t>0,\\ u(x,0) & = \int\sp \infty\sb 0 h(x,t)u(x,t)dt+ f(x),\quad x\in \Omega,\endaligned$$ is considered, where $\Omega$ is a bounded domain in $\bbfR\sp n$, $L$ is a uniformly parabolic operator with continuous and bounded coefficients. The solvability of the problem is shown using comparison arguments.
[S.Tersian (Russe)]

MSC 2000:: *35K60 (Nonlinear) BVP for (non)linear parabolic equations
35B40 Asymptotic behavior of solutions of PDE
35B50 Maximum principles (PDE)

Keywords: semilinear parabolic equations; nonlocal initial conditions; comparison arguments

Cited in: Zbl 1217.34103

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