A Maximum Principle for Periodic Solutions of the Telegraph Equation
نویسندگان
چکیده
منابع مشابه
A Maximum Principle for Periodic Solutions of the Telegraph Equation
Let L s L u be a linear differential operator acting on functions u: V a R that are defined on a fixed manifold V. These functions will belong to a Ž . certain family B ; F V, R , and the definition of B may include some boundary conditions or other requirements that must be satisfied by any function u g B. It is said that L satisfies the maximum principle if the differential inequality L u G 0...
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A maximum principle is proved for the weak solutions u ∈ L∞(R× T3) of the telegraph equation utt − xu + cut + λu = f (t, x), in space dimension three, when c > 0, λ ∈ (0, c2/4] and f ∈ L∞(R × T3) (Theorem 1). The result is extended to a solution and a forcing belonging to a suitable space of bounded measures (Theorem 2). Those results provide a method of upper and lower solutions for the semili...
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The existence of time-bounded solutions of nonlinear bounded perturbations of the telegraph equation with Neumann boundary conditions has recently been considered in [1]. The approach is based upon a Galerkin method combined with the use of some Lyapunov functionals. On the other hand, it has been proved in [7] that a maximum principle holds for the doubly 2π-periodic solutions of the telegraph...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1998
ISSN: 0022-247X
DOI: 10.1006/jmaa.1998.5921