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In this paper, we investigated the extinction, positivity, and decay estimates of the solutions to the initial-boundary value problem of the semilinear parabolic equation with nonlinear gradient source and interior absorption terms by using the integral norm estimate method. We found that the decay estimates depend on the choices of initial data, coefficients and domain, and the first eigenvalue of the Laplacean operator with homogeneous Dirichlet boundary condition plays an important role in the proofs of main results.
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참고문헌 (16)
참고문헌 신청
L. Alfonsi / 1992 / Blow up in Rn for a parabolic equation with a damping nonlinear gradient term / Progr. Nonlinear Differential Equations Appl 7:1~20
L. Amour / 1998 / Global existence and decay for viscous Hamilton-Jacobi equations / Nonlinear Anal. TMA 31:621~628
J. Bebernes / 1989 / Mathematical Problems from Combustion Theory / Springer-Verlag
S. Benachour / 2007 / Decay estimates for a viscous Hamilton-Jacobi equation with homogeneous Dirichlet boundary conditions / As-ymptotic Anal 51:209~229
S. L. Chen / 1998 / The extinction behavior of solutions for a reaction-diffusion equation / J. Math. Research and Exposition 18:583~586
L. Amour / 1998 / Global existence and decay for viscous Hamilton-Jacobi equations / Nonlinear Anal. TMA 31:621~628
J. Bebernes / 1989 / Mathematical Problems from Combustion Theory / Springer-Verlag
S. Benachour / 2007 / Decay estimates for a viscous Hamilton-Jacobi equation with homogeneous Dirichlet boundary conditions / As-ymptotic Anal 51:209~229
S. L. Chen / 1998 / The extinction behavior of solutions for a reaction-diffusion equation / J. Math. Research and Exposition 18:583~586
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