Khong Thi Thao Uyen, Nguyen Anh Triet, Le Thi Phuong Ngoc

In this paper, we consider the Robin-Dirichlet problem for a system of nonlinear pseudoparabolic
equations with viscoelastic term. By the Faedo-Galerkin method, we first prove
the existence and uniqueness of solution for the problem. Next, we give a sufficient condition
to get the global existence and decay of the weak solution. Finally, by the concavity method,
we prove the blow-up result of the solution when the initial energy is negative. Furthermore,
we establish here the lifespan of the solution by finding the upper bound and the lower bound
for the blow-up time.

Bui Duc Nam, Huynh Van Dung, Le Tuan Khai

In this paper, the Neumann-Dirichlet boundary problem for a system of nonlinear viscoelastic
equations of Kirchhoff type with Balakrishnan-Taylor term is considered. At
first, a local existence is established by the linear approximation together with the Faedo-
Galerkin method. Then, by establishing several reasonable conditions and suitable energy
inequalities, the solution of the problem admits a general decay in time.

Le Huu Ky Son, Nguyen Le Thi

This paper is devoted to the study of a Kirchhoff wave equation with a viscoelastic
term in an annular associated with homogeneous Dirichlet conditions. At first, by
applying the Faedo-Galerkin, we prove existence and uniqueness of the solution of the
problem considered. Next, by constructing Lyapunov functional, we establish a sufficient
condition such that any global weak solution is general decay as t → +∞.

Nguyen Huu Can, Nguyen Van Tien, Mai Quang Vinh

In this work, we focus on investigating ill-posed problems (according to the definition
given by Hadamard) in the topic of its application. Specifically, we present some theories
about the properties of the ill-posed problem in image processing. By using discrete
Fourier transform and fast Fourier transform methods, we present several results on
image processing topic. Finally, some illustrative examples are presented through algorithms
running on Python software.

Nguyen Dinh Huy, Nguyen Anh Tuan

In the current work, we study a Cauchy problem for a time-fractional pseudo-parabolic
equation with a globally Lipschitz source term. We prove the unique existence of a mild
solution to the problem, by the common Banach fixed point theorem. This solution is
then verified that exists globally in time by Gr¨onwall’s inequality. Compare to previous
works about the similar issuse, we approach in a way that does not require using
weighted spaces. Although our approach share a similar spirit to previous studies, our
method seems to be more precise and natural.

Ly Anh Duong, Le Huu Ky Son, Le Thi Phuong Ngoc

In this paper, we consider the Dirichlet problem for a wave equation of Kirchhoff-
Carrier type with a nonlinear viscoelastic term. It consists of two main parts. In Part
1, we establish existence and uniqueness of a weak solution by applying the Faedo-
Galerkin method and the standard arguments of density corresponding to the regularity
of initial conditions. In Part 2, we give a sufficient condition for the global existence
and exponential decay of the weak solutions by defining a modified energy functional
together with the technique of Lyapunov functional.

Doan Thi Nhu Quynh, Ho Thai Lyen, Huynh Ai Trieu, Nguyen Thanh Sang

The report deals with the Robin problem for a nonlinear wave equation with viscoelastic
term. Under some suitable conditions, we establish a high-order iterative scheme and
then prove that the scheme converges to the weak solution of the original problem along
with the error estimate. This result extends the result in [9].

Nguyen Vu Dzung, Tran Trinh Manh Dung

In this paper, we study the Robin-Dirchlet problem (Pn) for a wave equation with the
term
1
n
Xn
i=1
u2( i−1
n , t), n ∈ N. First, for each n ∈ N, under suitable conditions, we prove
the local existence and uniqueness of the weak solution un of (Pn). Next, we prove that
the sequence of solutions un of (Pn) converges strongly in appropriate spaces to the weak
solution u of the problem (P), where (P) is defined by (Pn) by replacing
1
n
Xn
i=1
u2( i−1
n , t)
by
Z 1
0
u2(y, t)dy. The main tools used here are the linearization method together with
the Faedo-Galerkin method and the weak compact method. We end the paper with a
remark related to a similar problem.

Vo Thi Tuyet Mai, Le Huu Ky Son, Tran Thi Kim Thoa

In this paper, we consider the Dirichlet boundary problem for a nonlinear wave equation
of Kirchhoff-Carrier-Love type as follow
utt − B
?
∥u(t)∥2 , ∥ux(t)∥2
(uxx + uxxtt)
= f(x, t, u, ux, ut, uxt) +
Xp
i=1
εifi(x, t, u, ux, ut, uxt)
for 0 < x < 1, 0 < t < T,
u(0, t) = u(1, t) = 0,
u(x, 0) = ˜u0(x), ut(x, 0) = ˜u1(x),
(1)
where ˜u0, ˜u1, B, f, fi (i = 1, · · · , p) are given functions, ε1, · · · , εp are small parameters
and ∥u(t)∥2 =
Z 1
0
u2 (x, t) dx, ∥ux(t)∥2 =
Z 1
0
u2
x (x, t) dx. First, a declaration of the
existence and uniqueness of solutions provided by the linearly approximate technique
and the Faedo-Galerkin method is presented. Then, by using Taylor’s expansion for
the functions B, f, fi, i = 1, · · · , p, up to (N + 1)th order, we establish a high-order
asymptotic expansion of solutions in the small parameters ε1, · · · , εp.

Nguyen Thi Khanh Hoa

In this paper, we restate some applications of logarithms in Richter scale, pH scale and
sound intensity level (Decibel scale).

Le Dinh Long, Danh Hua Quoc Nam, Vo Ngoc Minh, Bui Dai Nghia

In this paper, we are interested in the problem of determining the source function forthe
Sobolev equation with fractional Laplacian. This problem is non-well-posed. We show theerror
estimate between the exact solution and the regularized solution with the observed data in Lb
spaces.

Ngo Ngoc Hung, Tran Thanh Binh, Nguyen Duc Phuong

In this work, we study the problem of finding the source function of the inhomogeneous
diffusion equations with conformable derivative c∂α
t u−Δu = f(x), 0 < α < 1, associate
with random noisy input data. This problem is ill-posed in the sense of Hadamard. In
order to regulate the instablity of the solution, we applied the truncation method and
estimated the error estimate between the exact solution and the regularized solution.

Nguyen Tuan Dat, Mai Quang Vinh

Enzymes are biodegradable catalysts naturally present in living organisms. Enzymes
can accelerate biochemical reactions by reducing the activation energy, and they are
not consumed during reaction processes. Numerous applications of enzymes have been
developed in biotechnology, industry, medicine, pharmaceuticals, food processing, biofuels,
and so on. In this study, we develop a mathematical model describing enzymatic
reactions with a Ping-Pong mechanism and competitive substrate inhibition. In order
to obtain insights into the model behaviors, we use Python software to obtain numerical
solutions for the model. Some discussions on the numerical results is provided. Finally,
we briefly discuss a potential application of the model and some future work.

Le Thi Mai Thanh, Pham Nguyen Nhat Khanh

In this paper, a high-order iterative scheme is established in order to get a convergent
sequence at a rate of order N, (N ≥ 2) to a local unique weak solution of a nonlinear
Kirchhoff-type wave equation associated with Robin conditions.

**Publisher**

Thu Dau Mot University, Viet Nam

**Honorary Editor-in-Chief and Chairman of the Editorial Board**

Assoc. Prof. Nguyen Van Hiep

**Deputy Editor-in-Chief**

PhD. Trần Hạnh Minh Phương

Thu Dau Mot University

Thu Dau Mot University

**Editorial Board**

Prof. Tran Van Doan

Fujen University, Taiwan

Fujen University, Taiwan

Prof. Zafar Uddin Ahmed

Vietnam National University Ho Chi Minh City

Vietnam National University Ho Chi Minh City

Prof.Dr. Phillip G.Cerny

The University of Manchester, United Kingdom

The University of Manchester, United Kingdom

Prof. Ngo Van Le

University of Social Sciences and Humanities (VNU-HCM)

University of Social Sciences and Humanities (VNU-HCM)

Prof. Bui The Cuong

Southern Institute of Social Sciences

Southern Institute of Social Sciences

Prof. Le Quang Tri

Can Tho University

Can Tho University

Assoc. Prof. Nguyen Van Duc

Animal Husbandry Association of Vietnam

Animal Husbandry Association of Vietnam

Assoc. Prof. Ted Yuchung Liu

National Pingtung University, Taiwan

National Pingtung University, Taiwan

PhD. Anita Doraisami

Economics Monash University, Australia

Economics Monash University, Australia

Prof. Dr. Andrew Seddon

Asia Pacific University of Technology & innovation (APU)

Asia Pacific University of Technology & innovation (APU)

Assoc. Prof. Le Tuan Anh

Thu Dau Mot University

Thu Dau Mot University

Prof. Abtar Darshan Singh

Asia Pacific University, Malaysia

Asia Pacific University, Malaysia

Prof.Dr. Ron W.Edwards

The University of Melbourne, Australia

The University of Melbourne, Australia

Assoc. Prof. Hoang Xuan Nien

Thu Dau Mot University

Thu Dau Mot University

PhD. Nguyen Duc Nghia

Vietnam National University Ho Chi Minh City

Vietnam National University Ho Chi Minh City

PhD. Bao Dat

Monash University (Australia)

Monash University (Australia)

PhD. Raqib Chowdhury

Monash University (Australia)

Monash University (Australia)

PhD. Nguyen Hoang Tuan

Thu Dau Mot University

Thu Dau Mot University

PhD. Nguyen Thi Lien Thuong

Thu Dau Mot University

Thu Dau Mot University

**Assistant**

Nguyen Thi Man

Thu Dau Mot University

Thu Dau Mot University