In this paper, we study the nonexistence of global weak solutions to the Cauchy problem of quasilinear pseudohyperbolic equations with damping term. The sufficient conditions for nonexistence of nontrivial global weak solutions is obtained in terms of exponents, singularities order and other parameters in the problem. The nonlinear capacity method is applied to prove nonexistence theorems. The proofs of our nonexistence theorems are based on deriving apriori estimates for the possible solutions to the problem by an algebraic analysis of the integral form of inequalities with an optimal choice of test functions. The result is extended to the case of coupled system of quasilinear pseudohyperbolic equations.
On the Unsolvability Conditions for Quasilinear Pseudohyperbolic Equations,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 15,
2, Article 40.
Available at: https://digitalcommons.pvamu.edu/aam/vol15/iss2/40