[PDF][PDF] Exponential decay of solutions of semilinear parabolic equations with nonlocal initial conditions
K Deng - Journal of Mathematical analysis and applications, 1993 - researchgate.net
… In this paper, we consider the nonlocal initial–boundary value problem … However, we are
more concerned here with the behavior of solutions of problem (1.1)-(1.3). To be specific,
letting U(t) = max , „ |u(x, t)| and restricting J |h(x, t)| dt s 1, we show that U(t) decays
monotonically and tends to zero exponentially fast as t – oo. Our discussion relies on the
classical comparison principle. For completeness, we also prove the existence and
uniqueness of u(x, t), since the arguments for the linear problem (1.4)-(1.6) appear not to apply. …
more concerned here with the behavior of solutions of problem (1.1)-(1.3). To be specific,
letting U(t) = max , „ |u(x, t)| and restricting J |h(x, t)| dt s 1, we show that U(t) decays
monotonically and tends to zero exponentially fast as t – oo. Our discussion relies on the
classical comparison principle. For completeness, we also prove the existence and
uniqueness of u(x, t), since the arguments for the linear problem (1.4)-(1.6) appear not to apply. …
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