a nonexistence result for a nonlinear pde with robin condition
Clicks: 11
ID: 204357
2006
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Abstract
Under the assumption λ>0 and f verifying f(x,y,0)=0 in D, 2F(x,y,u)−uf(x,y,u)≥0, u≠0, and if Ω=R×D, we show the convexity of function E(t)=∬D|u(t,x,y)|2dxdy, where u:Ω→ℝ is a solution of problem λ(∂2u/∂t2)−(∂/∂x)(p(x,y)(∂u/∂x))−(∂/∂y)(q(x,y)(∂u/∂y))+f(x,y,u)=0 in Ω, u+ε(∂u/∂n)=0 on ∂Ω, considered in H2(Ω)∩L∞(Ω), p,q:D¯→ℝ are two nonnull functions on D, ε is a positive real number, and D=]a1,b1[×]a2,b2[, (F(x,y,s)=∫0sf(x,y,t)dt).
| Reference Key |
khodja2006internationala
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|---|---|
| Authors | ;Brahim Khodja |
| Journal | structural engineering and mechanics |
| Year | 2006 |
| DOI |
10.1155/IJMMS/2006/62601
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| URL | |
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