On nonhomogeneous biharmonic equations involving critical Sobolev exponent.
Self-similar solutions of convection-diffusion processes.
Nonexistence of global solutions of nonlinear wave equations.
Absence of global solutions to a class of nonlinear parabolic inequalities
We study the absence of nonnegative global solutions to parabolic inequalities of the type , where , 0 < β ≤ 2, is the β/2 fractional power of the Laplacian. We give a sufficient condition which implies that the only global solution is trivial if p > 1 is small. Among other properties, we derive a necessary condition for the existence of local and global nonnegative solutions to the above problem for the function V satisfying , where a ≥ 0, b > 0, p > 1 and V₊(x): = maxV(x),0. We...
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