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Positivity, Trotter Products, and Blow-up
We give a new approach to blow-up results for nonlinear evolution equations of the form u ( t ) = Au ( t ) +Φ( u ( t )) on ordered Banach spaces, using the...
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New exact solutions to KdV equations with variable coefficients or forcing
Jacobi elliptic function expansion method is extended to construct the exact solutions to another kind of KdV equations, which have variable...
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An a priori error estimate for finite element discretizations in nonlinear elasticity for polyconvex materials under small loads
We prove optimal a priori error estimates in W 1,p for finite element minimizers of polyconvex energy functionals with small applied loads. The proof...
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Level set methods based on distance function
Some basic problems on the level set methods were discussed, such as the method used to preserve the distance function, the existence and uniqueness...
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Existence and nonexistence results for reaction-diffusion equations in product of cones
Problems of existence and nonexistence of global nontrivial solutions to quasilinear evolution differential inequalities in a product of cones are...
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The Lax-Mizohata Theorem for Nonlinear Gauze Invariant Equations
We prove that ifthe Cauchy problem for the nonlinear partial differential equation is well-posed in a neighbourhood of a given solution, then all the...
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Gain of regularity for semilinear Schrödinger equations
We discuss local existence and gain of regularity for semilinear Schrödinger equations which generally cause loss of derivatives. We prove our...
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Well-posedness of the cauchy problem for the coupled system of the Schrödinger-KdV equations
This paper is devoted to the study of the Cauchy problem for the coupled system of the Schrödinger-KdV equations which describes the nonlinear...
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Temperature-dependent hysteresis in one-dimensional thermovisco-elastoplasticity
In this paper, we develop a thermodynamically consistent description of the uniaxial behavior of thermovisco-elastoplastic materials for which the...
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Nonlinear behavior of a gallo** cable
This paper presents the numerical experiment of a discretized loaded cable with periodic forcing. There appeared to be various type of nonlinear...
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On Strongly Interacting Internal Solitary Waves
The Cauchy problem and global well-posedness for a mathematical model of the strong interaction of two-dimensional, long, internal gravity waves...
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