This is a continuation of our study [Uhlmann-Zhai, JMPA, 2021] on an inverse boundary value problem for a nonlinear elastic wave equation. We prove that all the linear and nonlinear coefficients can be recovered from the displacement-to-traction map,...
Mar 20, 2022 · The first technique of solving an differential equation introduced in my course is separation of variables, with which often you cannot solve for functions with R as their domain (since â¦
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Jan 8, 2017 · The equation for your reflected line can be constructed using the point-slope form, $y=m (x-x_Q)+y_Q$. The point $ (x_Q,y_Q)$ is easily obtained as the intersection of your "mirror" line (the â¦
Sep 19, 2017 · What does α - β equal if a quadratic equation has roots of α and β Ask Question Asked 8 years, 5 months ago Modified 8 years, 5 months ago
May 28, 2013 · I love your answer for a line equation in the form of z = f (x, y)... Unfortunately calculating square roots can be impractical from the calculational standpoint and hence I really doubt any â¦
Existence of finite-time blow ups in the classical one-dimensional nonlinear Schrödinger equation (NLS) (1) i \partial_t u + u_{x x} + |u|^{2r} u = 0, u(x,0) = u_0(x) has been one of the central problems in the studies of the singularity formati...
This work presents a comparative study to numerically compute impulse approximate controls for parabolic equations with various boundary conditions. Theoretical controllability results have been recently investigated using a logarithmic convexity est...
A large class of Type II fluid solutions to Einstein field equations in N-dimensional spherical spacetimes is found, wich includes most of the known solutions. A family of the generalized collapsing Vaidya solutions with homothetic self-similarity,...
varying the spinor ψ ¯ ( x ) {\displaystyle {\bar {\psi }}(x)} . Meanwhile, the adjoint Dirac equation is acquired by varying the adjoint spinor ψ ( x ) {\displaystyle
(2.10) Suppose that we have a left handed spinor uL(p) that satisfies the Weyl equation. We can use it to construct a spinor that satisfies the Weyl equation for the right-handed spinor.
We study the linear profile decomposition for the Airy type equation, where the associated Strichartz inequality corresponds to the Fourier extension inequality on the odd curve $ξ^{\ell}$. We also investigate an inhomogeneous case, modeled by the o...
The analytic continuation of the Lippmann-Schwinger bras and kets is obtained and characterized. It is shown that the natural mathematical setting for the analytic continuation of the solutions of the Lippmann-Schwinger equation is the rigged Hilbe...
Isebree Moens (1846–1891), Dutch physician and physiologist Moens–Korteweg equation, biomechanic equation derived by Adriaan Isebree Alex Moens (born 1959)
Multi-dimensional breakage is a ubiquitous phenomenon in natural systems, yet the systematic discovery of underlying governing equations remains a long-standing challenge. Current inverse solution techniques are restricted to one-dimensional cases an...
In this paper we employ the Renormalization Group (RG) method to study higher order corrections to the long-time asymptotics of a class of nonlinear integral equations with a generalized heat kernel and with time-dependent coefficients. This is a fol...
This paper studies mean-field control problems with state-control joint law dependence and Poissonian common noise. We develop the stochastic maximum principle (SMP) and establish its connection to the Hamiltonian-Jacobi-Bellman (HJB) equation on the...
The Heisenberg, interaction, and Schrödinger pictures of motion are considered in Lagrangian (canonical) quantum field theory. The equations of motion (for state vectors and field operators) are derived for arbitrary Lagrangians which are polynomi...
We propose a hydridizable discontinuous Galerkin (HDG) method for solving the Cahn-Hilliard equation. The temporal discretization can be based on either the backward Euler method or the convex-splitting method. We show that the fully discrete scheme...