In this paper, we study, for the first time, the nonexistence of solutions to systems of parabolic differential inequalities in 2D exterior domains with Dirichlet and Neumann boundary conditions. Our obtained results complete those derived recently by Yuhua Sun [Nonexistence results for systems of elliptic and parabolic differential inequalities in exterior domains of , Pacific Journal of Mathematics. 293(1) (2018) 245–256] in the N-dimensional case, , under Dirichlet boundary condition.
D.G.Aronson and H.F.Weinberger, Multidimensional nonlinear diffusion arising in population genetics, Adv. in Math.30(1) (1978), 33–76. doi:10.1016/0001-8708(78)90130-5.
2.
C.Bandle and H.A.Levine, On the existence and nonexistence of global solutions of reaction-diffusion equations in sectorial domains, Trans. Amer. Math. Soc.316(2) (1989), 595–622. doi:10.1090/S0002-9947-1989-0937878-9.
3.
C.Bandle, H.A.Levine and Q.S.Zhang, Critical exponents of Fujita type for inhomogeneous parabolic equations and systems, J. Math. Anal. Appl.251 (2000), 624–648. doi:10.1006/jmaa.2000.7035.
4.
H.Fujita, On the blowing up of solutions of the Cauchy problem for , J. Fac. Sci. Univ. Tokyo. Sect. I13 (1966), 109–124.
5.
K.Hayakawa, On nonexistence of global solutions of some semilinear parabolic differential equations, Proc. Japan Acad.49 (1973), 503–505. doi:10.3792/pja/1195519254.
6.
G.G.Laptev, Nonexistence results for higher-order evolution partial differential inequalities, Proc. Amer. Math. Soc.131(2) (2003), 415–423. doi:10.1090/S0002-9939-02-06665-0.
7.
E.Mitidieri and S.I.Pohozaev, A priori estimates and the absence of solutions of nonlinear partial differential equations and inequalities, Tr. Mat. Inst. Steklova.234 (2001), 3–383(In Russian).
8.
Y.Sun, Nonexistence results for systems of elliptic and parabolic differential inequalities in exterior domains of , Pacific Journal of Mathematics.293(1) (2018), 245–256. doi:10.2140/pjm.2018.293.245.
9.
Q.S.Zhang, A general blow-up result on nonlinear boundary-value problems on exterior domains, Proc. Roy. Soc. Edinburgh Sect. A131(2) (2001), 451–475. doi:10.1017/S0308210500000950.
