On existence and nonexistence of global solutions of Cauchy–Goursat problem for nonlinear wave equations
Copyright policy )On existence and nonexistence of global solutions of Cauchy–Goursat problem for nonlinear wave equations
The Cauchy-Goursat initial characteristic problem for the equation \(u_{tt}-u_{xx}+\lambda | u| ^{\alpha }u=f(x,t)\) is treated. The author defines a strong generalized solution of the problem and investigates the existence and the nonexistence of this solution in dependence on the numbers \(\alpha \) and \(\lambda .\)
Nonlinear wave equations, Applied Mathematics, Blow-up, global solvability, Cauchy–Goursat problem, Global and local solvability, blow-up, strong generalized solution, Analysis, Second-order nonlinear hyperbolic equations
Nonlinear wave equations, Applied Mathematics, Blow-up, global solvability, Cauchy–Goursat problem, Global and local solvability, blow-up, strong generalized solution, Analysis, Second-order nonlinear hyperbolic equations
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