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Exact estimates of amplitude and support of unbounded solutions of a nonlinear heat equation with a source. (Russian) Zbl 0707.35007
Estimates for the $$L^{\infty}$$-norm and for the support of the solution of the parabolic equation: $$u_ t=(u^{\nabla}u_ x)_ x+u^{\sigma +1}$$, $$u(0,x)=u_ 0(x)\geq 0$$, $$\sigma >0$$ are given.
Reviewer: D.Tătaru

MSC:
 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 35K55 Nonlinear parabolic equations 35B45 A priori estimates in context of PDEs