Exact estimates of amplitude and support of unbounded solutions of a nonlinear heat equation with a source. (Russian) Zbl 0707.35007

Galaktionov, V. A.

Zh. Vychisl. Mat. Mat. Fiz. 30, No. 3, 438-448 (1990).

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

Keywords:

nonlinear heat equation; \(L^{\infty }\)-norm; support