The aim of this article is to study the dynamic Von-Karman model coupledwith thermoelastic equations without rotational terms, subject a thermal dissipation. We establish existence as well uniqueness weak solution related model. At end, we apply finite difference method for approximating our problem.

Abstract In this paper, assuming the initial-boundary datum belonging to suitable Sobolev and Lebesgue spaces, we prove global existence result for a (possibly sign changing) weak solution Cauchy–Dirichlet problem doubly nonlinear parabolic equations of form $$\begin{aligned} \partial _t\left( |u|^{q-1}u\right) -\Delta _p u=0\quad \text {in}\,\,\,\Omega _\infty , \end{aligned}$$ <mml:math xmlns...

We treat the evolution as gradient flow with respect to the Wasserstein distance on a special manifold and construct the weak solution for the initial-value problem by using a standard time-discretized implicit scheme. The concept of Wasserstein kernel associated with one-dimensional diffusion problems with Neumann boundary conditions is introduced. Based on this, features of the initial data a...

If p ∈ (0, N N−2α ), α ∈ (0, 1), k > 0 and Ω ⊂ R is a bounded C domain containing 0 and δ0 is the Dirac measure at 0, we prove that the weak solution of (E)k (−∆) u + u = kδ0 in Ω which vanishes in Ω is a weak singular solution of (E)∞ (−∆) u + u = 0 in Ω \ {0} with the same outer data. Furthermore, we study the limit of weak solutions of (E)k when k → ∞. For p ∈ (0, 1+ 2α N ], the limit is inf...