Abstract We consider a one-Laplace equation perturbed by p -Laplacian with $$1<p<\infty $$ 1 < p ∞ . prove that weak solution is continuously differentiable $$(C^1)$$ ( C ...

We present an adaptive animation method for electrical discharges. Electric discharges can be simulated using the dielectric breakdown model. Regular discretization of the governing Laplace equation leads to huge equation systems, and the computational cost of solving the equations quickly becomes prohibitive at high resolutions, especially for simulations in 3D. In contrast, our method discret...

<p style='text-indent:20px;'>We study the inverse problem for fractional Laplace equation with multiple nonlinear lower order terms. We show that direct is well-posed and uniquely solvable. More specifically, unknown nonlinearities can be determined from exterior measurements under suitable settings.</p>

Abstract Based on the recent work [4] for compact potentials, we develop the spectral theory for the one-dimensional discrete Schrödinger operator Hφ = (−∆+ V )φ = −(φn+1 + φn−1 − 2φn) + Vnφn. We show that under appropriate decay conditions on the general potential (and a nonresonance condition at the spectral edges), the spectrum of H consists of finitely many eigenvalues of finite multiplicit...

In this paper we study intermittency for the parabolic Anderson equation ∂u/∂t = κ∆u + ξu, where u : Z d × [0, ∞) → R, κ is the diffusion constant, ∆ is the discrete Laplacian, and ξ : Z d × [0, ∞) → R is a space-time random medium. We focus on the case where ξ is γ times the random medium that is obtained by running independent simple random walks with diffusion constant ρ starting from a Pois...

The generalized coupled thermo-viscoelasticity of hollow sphere subjected to thermal symmetric shock load is presented in this paper. To overcome the infinite speed of thermal wave propagation, the Lord-Shulman theory is considered. Two coupled equations, namely, the radial equation of motion and the energy equation of a hollow sphere are obtained in dimensionless form. Resulting equations are ...