AbstractIn this paper we consider the heat equationut=Δuin an unbounded domain Ω⊂RNwith a partly Dirichlet conditionu(x,t)=0 and a partly Neumann conditionuν=upon the boundary, wherep>1 and ν is the exterior unit normal on the boundary. It is shown that for a sectorial domain inR2and anorthantdomain inRNthere exists an explicit critical exponentpc(Ω)>1 such that all positive solutions blow up in finite time whenp∈(1,pc] while there exist positive global solutions ifp>pcand initial data are suitably small. All our blowup results include the critical case
We construct global unbounded solutions for the critical nonlinear heat equation on a bounded smooth...
AbstractWe establish a universal upper bound on the initial blow-up rate for all positive classical ...
We study a nonlinear one dimensional heat equation with nonmonotone perturbation and with mixed boun...
AbstractIn this paper we consider the heat equationut=Δuin an unbounded domain Ω⊂RNwith a partly Dir...
In this study, we consider the nonlinear heat equation $$displaylines{ u_{t}(x,t) = Delta u(x,t) + u...
Abstract. In this study, we consider the nonlinear heat equation ut(x, t) = ∆u(x, t) + u(x, t) p in...
. In this paper, we consider the system u t = \Deltau; v t = \Deltav x 2 R N + ; t ? 0; \Gamma ...
We show that for many regions of product type $D=D_1 \times D_2$ the critical exponent of blowup for...
We show that for many regions of product type $D=D_1 \times D_2$ the critical exponent of blowup for...
Consider the nonlinear heat equation vt − Δv = |v|p−1v in a bounded smooth domain Ω ⊂ Rn with n > 2...
AbstractThis note establishes the blow up estimates near the blow up time for a system of heat equat...
AbstractWe consider the initial–boundary value problem for the heat equation with a nonlinear bounda...
AbstractIn this paper we study the large time behavior of positive solutions of the heat equation un...
AbstractConsider the equation(0.1)ut=Δu−Vu+aupin Rn×(0,T);u(x,0)=ϕ(x)≩0in Rn, where p>1, n⩾2, T∈(0,∞...
We construct global unbounded solutions for the critical nonlinear heat equation on a bounded smooth...
We construct global unbounded solutions for the critical nonlinear heat equation on a bounded smooth...
AbstractWe establish a universal upper bound on the initial blow-up rate for all positive classical ...
We study a nonlinear one dimensional heat equation with nonmonotone perturbation and with mixed boun...
AbstractIn this paper we consider the heat equationut=Δuin an unbounded domain Ω⊂RNwith a partly Dir...
In this study, we consider the nonlinear heat equation $$displaylines{ u_{t}(x,t) = Delta u(x,t) + u...
Abstract. In this study, we consider the nonlinear heat equation ut(x, t) = ∆u(x, t) + u(x, t) p in...
. In this paper, we consider the system u t = \Deltau; v t = \Deltav x 2 R N + ; t ? 0; \Gamma ...
We show that for many regions of product type $D=D_1 \times D_2$ the critical exponent of blowup for...
We show that for many regions of product type $D=D_1 \times D_2$ the critical exponent of blowup for...
Consider the nonlinear heat equation vt − Δv = |v|p−1v in a bounded smooth domain Ω ⊂ Rn with n > 2...
AbstractThis note establishes the blow up estimates near the blow up time for a system of heat equat...
AbstractWe consider the initial–boundary value problem for the heat equation with a nonlinear bounda...
AbstractIn this paper we study the large time behavior of positive solutions of the heat equation un...
AbstractConsider the equation(0.1)ut=Δu−Vu+aupin Rn×(0,T);u(x,0)=ϕ(x)≩0in Rn, where p>1, n⩾2, T∈(0,∞...
We construct global unbounded solutions for the critical nonlinear heat equation on a bounded smooth...
We construct global unbounded solutions for the critical nonlinear heat equation on a bounded smooth...
AbstractWe establish a universal upper bound on the initial blow-up rate for all positive classical ...
We study a nonlinear one dimensional heat equation with nonmonotone perturbation and with mixed boun...