Partial Differential Equations And Systems Not Solvable With Respect To The Highest-Order Derivative

Numerical solution of two-dimensional integral-algebraic systems using Legendre functions

“…In this section we describe a numerical method to solve problem (1). We assume that the sufficient conditions for existence of solution, discussed in [2], are satisfied.…”

“…where A(t, x) and K(t, x, τ, s) are n × n matrices, f (t, x) is a given vector function and u(t, x) is the unknown. This kind of problems may arise from the analysis of some classes of differential-algebraic systems of partial differential equations [1] and in the modeling of certain heat conduction processes.…”

Existence of Solutions in Quasi-Banach Spaces for Evolutionary Sobolev Type Equations in Relatively Radial Case

“…Refer to a vector function u ∈ C ∞ (R + ; U) satisfying (6) pointwise as a (classical) solution to this equation. Refer to a solution u = u(t) to (6) as a solution to a weak initial value problem (in the sense of Krein) whenever in addition lim t→0+ u(t) = u 0 (7) for some u 0 ∈ U.…”

“…2] and extended to Fréchet spaces in [6]. The equations of the form (3) appeared for the first time at the end of 19th century in Poincaré's works, and in the second half of the 20th century Sobolev began their systematic study (see [7] for a great survey). Since the interest in Sobolev-type equations is growing fast recently (see [8] - [11] for instance), it becomes necessary to consider them in quasi-Banach spaces.…”

On adaptive mesh for the initial boundary value singularly perturbed delay Sobolev problems

“…Degenerate differential equations of Sobolev type were studied from an abstract point of view in Favini and Yagi [16]. In many important studies, results were obtained for systems of equations unsolved with respect to the highest derivative with respect to time [17]. Various numerical treatments of equations of this type in the regular cases (i.e., in the absence singularity) have been considered in many studies [15,[18][19][20].…”