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On some properties of generalized solutions of the wave equation in the classes L p and W p 1 for p ≥ 1 For each p ≥ 1, in closed analytic form, we establish the existence of a unique generalized solution in L p of the mixed ... V.,A.,Il’in,... - 《Differential Equations...
The knowledge of the wave equation is of fundamental importance for a good and satisfying understanding of the phenomena of wave propagation. However, it is unsatisfactory and inefficient to work with the full anisotropic wave equation in media that exhibit certain symmetries. We derive a specific ...
Stability analysis of a second-order difference scheme for the time-fractional mixed sub-diffusion and diffusion-wave equation This study investigates a class of initial-boundary value problems pertaining to the time-fractional mixed sub-diffusion and diffusion-wave equation (SDDWE... AA Alikhanov,MS...
The Schrödinger equation was solved for the energy values of the described systems, in part by providing approximate solutions to integrals that the authors could not compute directly. In the end, Heitler and London obtained tidy expressions for the molecular energy levels:11 (5)ES=HII+HIII1+...
Traveling wave solutions are a class of invariant solutions which are critical for shallow water wave equations. In this paper, traveling wave solutions for two perturbed KP-MEW equations with a local delay convolution kernel are examined. The model equation is reduced to a planar near-Hamiltonian...
@@ -121,6 +121,8 @@ class ElasticWaveEquationSEM : public WaveSolverBase static constexpr char const * sourceForceString() { return "sourceForce"; } static constexpr char const * sourceMomentString() { return "sourceMoment"; } static constexpr char const * useVtiString() { return "us...
We first introduce the influence function (or dual solution) associated to the quantity of interest, , as the solution of the dual problem (34a)(34b)(34c) We note that this is a well-posed backward elastic equation with zero data at the final time and a time-independent force term. As...
The existence of an almost periodic “minimal-energy blowup solution” to the wave maps equation in the energy class, if this equation is such that singularities can form in finite time. The non-existence of any non-trivial degenerate maps into hyperbolic space in the energy class, where “...
In this paper, the blow-up and asymptotic behavior of global solution of damped wave equation with dynamic boundary condition are discussed. By the convexity lemma and unstable set, the sufficient con- dition of the solution of the wave equation with negative and positive initial energy respectivel...