Distribution Solution of Some Nonlinear PDEs Related to the Elastic Bessel Klein-Gordon Wave Operator
Keywords:Generalized function, Tempered distribution, Elastic wave equation, Nonlinear partial differential equation
AbstractThis paper studies the existence and uniqueness of the solution to the boundary value problem for the nonlinear partial differential equation. We are particularly interested in the elastic Bessel-Helmholtz and elastic Bessel Klein-Gordon wave operators. To attain the results, the distribution theory (the generalized function theory), the iteration method and the classical Schauder estimates are applied. The solution is consequently in the form of tempered distribution (slow growth function).
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