This investigation focuses on identifying weak solutions for a nonlinear diffusion equation that includes $p(u)$-Laplacian-like operators. By imposing specific conditions on the initial value, we derive our result using a time-discrete approach in conjunction with a singular perturbation technique and Schauder's fixed-point theorem.
In this paper, we study the additivity property of the transition energy in a finite volume. In particular, we show how this property can be applied to solve the well-known problem of finding the conditions under which a given system of probability distributions parameterized by boundary conditions is a system of conditional probabilities for some finite random field (joint probability distribution).
In this paper, we consider the blow-up behavior of linearly implicit L1 method for fractional ordinary differential equations. Based on Nakagawa's criteria, a suitable adaptive step strategy is introduced. The existence of global numerical solution is proved. Moreover, we show that the finite blow-up behaviors are replicated for any positive solution. Finally, some numerical examples are given to test the main result.
The Sturm-Liouville wavelet transform (SLWT) is a novel addition to the class of Sturm-Liouville transforms, which has gained a respectable status in the realm of time-frequency signal analysis within a short span of time. Given that the study of time-frequency analysis is of both theoretically interesting and practically useful, the aim of this paper is to explore a class of quantitative uncertainty principles (UP) associated with SLWT, including Faris local-type UP, Shannon-type UP, Donoho-Stark-type UP and Benedicks-type UP.
We consider three-dimensional Lorentzian Egorov and epsilon-spaces and show that the existence of proper biharmonic helices in these manifolds is highly constrained and closely tied to the causal character of the Frenet frame. In particular, we prove that no proper biharmonic helices exist in Egorov spaces unless the space is flat and the normal vector is spacelike. Furthermore, we establish that no proper biharmonic helices exist in threedimensional epsilon-spaces.
