Global existence for small data Cauchy problem of semilinear wave equations with scaling invariant damping in 3-D is established this work, assuming that the are radial and constant front belongs to [1.5,2). The proof based on a weighted L2−L2 estimate inhomogeneous equation, which by interpolating between energy Morawetz type estimate.

We establish elliptic regularity for nonlinear, inhomogeneous Cauchy-Riemann equations under weak assumptions, and give a counterexample in a borderline case. In some cases where the inhomogeneous term has a separable factorization, the solution set can be explicitly calculated. The methods also give local parametric formulas for pseudoholomorphic curves with respect to some continuous almost c...

The problems of unique solvability initial for linear inhomogeneous equations a general form with several Gerasimov-Caputo fractional derivatives in Banach spaces are investigated. Cauchy problem is considered an equation solved respect to the highest derivative containing bounded operators at lowest derivatives. solution presented use Dunford-Taylor type integrals. obtained result allowed us s...

Abstract. We use a new variational method—based on the theory of anti-selfdual Lagrangians developed in [2] and [3]—to establish the existence of solutions of convex Hamiltonian systems that connect two given Lagrangian submanifolds in R . We also consider the case where the Hamiltonian is only semi-convex. A variational principle is also used to establish existence for the corresponding Cauchy...

We consider the inverse problem of determining an inclusion contained in a body for Schrödinger type equation by means local Cauchy data. Both and are made inhomogeneous anisotropic materials. Under mild priori assumptions on unknown inclusion, we establish logarithmic stability estimate terms In view possible applications, also provide ad-hoc misfit functional.

n this paper, we apply Picard’s Iteration Method followed by Adomian Decomposition Method to solve a nonlinear Singular Cauchy Problem of Euler- Poisson- Darboux Equation. The solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by Carroll and Showalter (1976)in the solution of Singular Cauchy Problem. 

Recently, a lot of progress has been made on the study for the spatially homogeneous Boltzmann equation without angular cutoff, cf. [2, 3, 8, 22] and references therein, which shows that the singularity of collision cross-section yields some gain of regularity in the Sobolev space frame on weak solutions for Cauchy problem. That means, this gives the C regularity of weak solution for the spatia...