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This paper deals with blow-up phenomena for an initial boundary value problem of a quasilinear parabolic equation with time-dependent coefficient in a bounded star-shaped region under nonlinear boundary flux. Using the auxiliary function method and differential inequality technique, we establish some conditions on time-dependent coefficient and nonlinear functions for which the solution u(x, t) exists globally or blows up at some finite time $t^*$. Moreover, some upper and lower bounds for $t^*$ are derived in higher dimensional spaces. Some examples are presented to illustrate applications of our results.
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참고문헌 (25)
참고문헌 신청
K. Baghaei / 2013 / Lower bounds for the blow-up time in the higher-dimensional nonlinear divergence form parabolic equations / C. R. Acad. Sci. Paris. Ser. I. 351:731~735
C. Bandle / 1998 / Blow-up in diffusion equations: A survey / J. Comput. Appl. Math. 97:3~22
J. Bebernes / 1989 / Mathematical Problems from Combustion Theory / Springer-Verlag
H. Brezis / 2011 / Functional Analysis, Sobolev Spaces and Partial Differential Equations / Springer-Verlag
C. Enache / 2011 / Blow-up phenomena for a class of quasilinear parabolic problems under Robin boundary condition / Appl. Math. Lett. 24:288~292
C. Bandle / 1998 / Blow-up in diffusion equations: A survey / J. Comput. Appl. Math. 97:3~22
J. Bebernes / 1989 / Mathematical Problems from Combustion Theory / Springer-Verlag
H. Brezis / 2011 / Functional Analysis, Sobolev Spaces and Partial Differential Equations / Springer-Verlag
C. Enache / 2011 / Blow-up phenomena for a class of quasilinear parabolic problems under Robin boundary condition / Appl. Math. Lett. 24:288~292
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