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Blow-up of the solution for higher-order Kirchhoff-type equations with nonlinear dissipation

100%
Gao Q., Li F., Wang Y.
Open Mathematics
|
2011
|
tom 9
|
nr 3
686-698
EN
In this paper, we consider the nonlinear Kirchhoff-type equation $$ u_{tt} + M(\left\| {D^m u(t)} \right\|_2^2 )( - \Delta )^m u + \left| {u_t } \right|^{q - 2} u_t = \left| {u_t } \right|^{p - 2} u $$ with initial conditions and homogeneous boundary conditions. Under suitable conditions on the initial datum, we prove that the solution blows up in finite time.
2
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Blow-up and global existence profile of a class of fully nonlinear degenerate parabolic equations

88%
Li J., Yin J., Jin C.
Open Mathematics
|
2011
|
tom 9
|
nr 6
1435-1447
EN
This paper is mainly concerned with the blow-up and global existence profile for the Cauchy problem of a class of fully nonlinear degenerate parabolic equations with reaction sources.
3
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Numerical investigation of a new class of waves in an open nonlinear heat-conducting medium

75%
Dimova M., Dimova S., Vasileva D.
Open Mathematics
|
2013
|
tom 11
|
nr 8
1375-1391
EN
The paper contributes to the problem of finding all possible structures and waves, which may arise and preserve themselves in the open nonlinear medium, described by the mathematical model of heat structures. A new class of self-similar blow-up solutions of this model is constructed numerically and their stability is investigated. An effective and reliable numerical approach is developed and implemented for solving the nonlinear elliptic self-similar problem and the parabolic problem. This approach is consistent with the peculiarities of the problems - multiple solutions of the elliptic problem and blow-up solutions of the parabolic one.
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