The linear heat equation with highly oscillating potential

Author:

Kombe Ismail

Abstract

In this paper we consider the following initial value problem: \[ { u t = H u + V ( x ) u a m p ; in  R N × ( 0 , T ) , u ( x , 0 ) = u 0 ( x ) 0 a m p ; on  R N × { t = 0 } , \begin {cases} \frac {\partial u}{\partial t}=-Hu+V(x)u & \text {in $\mathbb {R}^N\times (0,T)$},\\ u(x,0) = u_0 (x)\geq 0 & \text {on $\mathbb {R}^N \times \{t=0\}$}, \end {cases} \] where H = Δ β | x | 2 sin ( 1 | x | α ) H=-\Delta -\frac {\beta }{|x|^2}\sin (\frac {1}{|x|^{\alpha }}) and 0 V L loc 1 ( R N ) 0\le V\in L_{\text {loc}}^1(\mathbb {R}^N) . Nonexistence of positive solutions is analyzed.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference12 articles.

1. Global behavior of the Cauchy problem for some critical nonlinear parabolic equations;Aguilar Crespo, J. A.;SIAM J. Math. Anal.,2000

2. The heat equation with a singular potential;Baras, Pierre;Trans. Amer. Math. Soc.,1984

3. Existence versus explosion instantanée pour des équations de la chaleur linéaires avec potentiel singulier;Cabré, Xavier;C. R. Acad. Sci. Paris S\'{e}r. I Math.,1999

4. Graduate Studies in Mathematics;Evans, Lawrence C.,1998

5. Hardy inequalities and some critical elliptic and parabolic problems;García Azorero, J. P.;J. Differential Equations,1998

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