A parabolic system of quasilinear equations. II. (English. Russian original) Zbl 0599.35085
Differ. Equations 21, 1049-1062 (1985); translation from Differ. Uravn. 21, No. 9, 1544-1559 (1985).
[For Part I, see ibid. 19, 1558-1574 (1983); translation from Differ. Uravn. 19, No.12, 2123-2140 (1983; Zbl 0556.35071).]
This paper deals with properties of the solution of a parabolic system of two quasilinear equations of the form \[ u_ t=\Delta u^{\nu +1}+v^ p,\quad v_ t=\Delta v^{\mu +1}+u^ q, \] where \(\mu\),\(\nu\),p,q are positive numbers. Let \(m=pq-(1+\mu)(1+\nu)\), then the case \(m\leq 0\) determines conditions for the global solvability of the boundary value problem and the other case gives a criterion for the location of the unbounded solutions of the Cauchy problem.
This paper deals with properties of the solution of a parabolic system of two quasilinear equations of the form \[ u_ t=\Delta u^{\nu +1}+v^ p,\quad v_ t=\Delta v^{\mu +1}+u^ q, \] where \(\mu\),\(\nu\),p,q are positive numbers. Let \(m=pq-(1+\mu)(1+\nu)\), then the case \(m\leq 0\) determines conditions for the global solvability of the boundary value problem and the other case gives a criterion for the location of the unbounded solutions of the Cauchy problem.
Reviewer: P.Chocholatý
MSC:
| 35K55 | Nonlinear parabolic equations |
| 35K40 | Second-order parabolic systems |
| 35B30 | Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs |
