NONEXISTENCE OF GLOBAL SOLUTIONS TO THE SYSTEM OF SEMILINEAR PARABOLIC EQUATIONS WITH BIHARMONIC OPERATOR AND SINGULAR POTENTIAL

In the domain Q'(R) = {x : vertical bar x vertical bar > R} x (0, +infinity) we consider the problem partial derivative u(1)/partial derivative t + Delta(2)u(1) - C-1/vertical bar x vertical bar(4) u(1) = vertical bar x vertical bar(sigma 1)vertical bar u(2 vertical bar)(q1), u(1)vertical bar(t=0) = u(10)(x) >= 0, partial derivative u(2)/partial derivative t + Delta(2)u(2) - C-2/vertical bar x vertical bar(4) u(2) = vertical bar x vertical bar(sigma 2)vertical bar u(1 vertical bar)(q2), u(2)vertical bar(t=0) = u(20)(x) >= 0, integral(infinity)(0) integral(partial derivative BR) u(i) ds dt >= 0, integral(infinity)(0) integral(partial derivative BR) Delta u(i) ds dt <= 0, where sigma(i) is an element of R, q(i) > 1, 0 <= C-i < (n(n-4)/4)(2), i = 1, 2. sufficient condition for the nonexistence of global solutions is obtained. The proof is based on the method of test functions.