A nonexistence result for a nonlinear PDE with Robin condition

作者：Brahim Khodja

来源：International Journal of Mathematics and Mathematical Sciences, 2006.

DOI：10.1155/ijmms/2006/62601

Under the assumption %26#x03BB;%26#x003E;0 and f verifying f(x,y,0)=0 in D, 2F(x,y,u)%26#x2212;uf(x,y,u)%26#x2265;0, u%26#x2260;0, and if %26#x03A9;=R%26#x00D7;D, we show the convexity of function E(t)=%26#x222C;D|u(t,x,y)|2dxdy, where u:%26#x03A9;%26#x2192;%26#x211D; is a solution of problem %26#x03BB;(%26#x2202;2u/%26#x2202;t2)%26#x2212;(%26#x2202;/%26#x2202;x)(p(x,y)(%26#x2202;u/%26#x2202;x))%26#x2212;(%26#x2202;/%26#x2202;y)(q(x,y)(%26#x2202;u/%26#x2202;y))

• 出版日期2006